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About: Prime ideal
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endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Prime_ideal">Prime ideal</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/ontology/ProgrammingLanguage">programming language</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime.</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/A_portion_of_the_lattice_of_ideals_of_Z_illustrating_prime,_semiprime_and_primary_ideals_SVG.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ca" >En matemàtiques, un ideal primer és un conjunt inclòs en un anell que té unes propietats semblants a les que tenen els nombres primers dins l'anell dels nombres enters. El concepte d'ideal primer té important rellevància, no només dins la pròpia teoria d'anells de l'àlgebra abstracta sinó també en teoria algebraica de nombres i en l'aritmètica modular.</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="cs" >Prvoideálem v okruhu je každý takový vlastní ideál , že pro libovolné dva ideály splňující (tedy jejichž součin je podmnožinou ) platí buď nebo . Jedná se o analogii prvočísel, u kterých lze obdobně vyslovit: Přirozené číslo je prvočíslem právě tehdy, pokud pro jakákoliv dvě přirozená čísla platí, že pokud dělí , pak buď dělí nebo dělí .</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >In der Ringtheorie ist ein Primideal eine Teilmenge eines Ringes, die sich ähnlich wie eine Primzahl als Element der ganzen Zahlen verhält.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="eo" >En ringo-teorio, prima idealo estas ĝeneraligo de la koncepto de primoj: ĝi estas tia idealo en komuta ringo, ke se iu produto apartenas al ĝi, tiam almenaŭ unu el la multiplikatoj apartenas al ĝi. En algebra geometrio, prima idealo respondas al punktoj en afinaj skemoj.</span><small> (eo)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >En la teoría de los anillos, una rama de la álgebra abstracta, el concepto de ideal primo es una generalización importante del concepto de número primo. Un ideal primo es un Ideal de un anillo conmutativo o no-conmutativo. Los ideales primos tienen una descripción más sencilla para los anillos conmutativos, por lo que distinguiremos los dos casos abajo.</span><small> (es)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >En algèbre commutative, un idéal premier d'un anneau commutatif unitaire est un idéal tel que le quotient de l'anneau par cet idéal est un anneau intègre. Ce concept généralise la notion de nombre premier à des anneaux à la structure moins simple d'accès que l'anneau des entiers relatifs. Ils jouent un rôle particulièrement important en théorie algébrique des nombres.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >素イデアル（英: prime ideal）は、環のイデアルで、ある条件を満たすものである。歴史的には、素数（素元）の概念の拡張としてデデキントによって代数体の整数環に対して定義された。整数環（一般にデデキント環）のすべてのゼロでない（整）イデアルは、素イデアルの有限個の積として（順序を除いて）一意的に書ける（イデアル論の基本定理）。スキームの理論は、図形の上の関数の成す環から下の空間を構成するという idea がもとになっているが、その時に、その環の素イデアルひとつひとつが、下の空間の点に対応する。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >환론에서 소 아이디얼(素ideal, 영어: prime ideal)은 아이디얼 가운데 소수와 같은 성질을 갖는 것들이다. 가환환의 소 아이디얼은 대수기하학에서 아핀 스킴의 부분다양체에 대응하며, 아핀 스킴의 위상 공간의 한 점을 이룬다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Ideał pierwszy – taki ideał właściwy pierścienia przemiennego z jedynką, dla którego z należenia do niego iloczynu dwóch danych elementów pierścienia wynika przynależność do niego choć jednego z czynników, tzn. ideał pierścienia nazywany jest pierwszym, gdy z należenia wynika, że lub Ideały pierwsze to w pewnym sensie te ideały, dla których zachodzi teza lematu Euklidesa o podzielności liczb całkowitych, tzn. odgrywają one rolę liczb pierwszych w teorii pierścieni. Pojęcie ideału pierwszego znajduje zastosowania w geometrii algebraicznej i teorii liczb. Z danym pierścieniem przemiennym z jedynką można w naturalny sposób stowarzyszyć pewną przestrzeń topologiczną, której punktami są ideały pierwsze, a zbiorami domkniętymi są zbiory wszystkich ideałów pierwszych zawierających ustalony podzbiór pierścienia. Przestrzeń ta nazywana jest spektrum pierwszym pierścienia i oznaczana symbolem Spec .</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="it" >In matematica, e precisamente nella teoria degli anelli, un ideale primo è un ideale che ha alcune proprietà che lo rendono simile ad un numero primo nell'anello degli interi. Sarà dapprima presentata la definizione in un anello commutativo, poiché in questo caso gli ideali primi hanno una caratterizzazione più semplice, poi la generalizzazione in un anello qualsiasi.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="nl" >In de abstracte algebra, een deelgebied van de wiskunde, is het begrip priemideaal een veralgemening van zowel een priemgetal als een . Priemidealen zijn "ondeelbaar" in de zin dat ze niet geschreven kunnen worden als product van twee andere idealen. Tenzij uitdrukkelijk anders vermeld, gaat dit artikel over priemidealen in een commutatieve ring met eenheidselement 1 verschillend van nul.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Первичный идеал является обобщением понятия простого числа в кольце целых чисел на произвольные (некоммутативные) кольца. Понятие простого идеала является частным случаем этого понятия.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pt" >Em álgebra, um ideal primo é um subconjunto de um anel que tem várias propriedades em comum com as de um número primo do anel dos inteiros. Os ideais primos para os inteiros são os conjuntos que contém todos os múltiplos de um número primo dado, juntamente com o ideal nulo. Ideais primitivos são primos, e ideais primos são tanto primários quanto semiprimos.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="sv" >Ett primideal är ett ideal P ≠ R i en kommutativ ring R, sådant att: för alla a och b i R. Om ringen R inte är kommutativ är P ett primideal, om det är ett äkta ideal och om det för ideal och sådana att gäller att antingen eller .</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >В абстрактній алгебрі простий ідеал — ідеал кільця, властивості якого схожі з властивостями простих чисел. Окрім теорії кілець поняття також часто використовується у алгебраїчній геометрії, де прості ідеали многочленів визначають афінні многовиди. Узагальненням поняття простого ідеала є примарний ідеал.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >在数学中，素理想（Prime ideal）是环的一个子集，与整数环中的素数共享许多重要的性质。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/A_portion_of_the_lattice_of_ideals_of_Z_illustrating_prime,_semiprime_and_primary_ideals_SVG.svg?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/A_portion_of_the_lattice_of_ideals_of_Z_illustrating_prime,_semiprime_and_primary_ideals_SVG.svg?width=300"><small>wiki-commons</small>:Special:FilePath/A_portion_of_the_latt..._and_primary_ideals_SVG.svg?width=300</a></span></li> </ul></td></tr><tr 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</ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type"><small>rdf:</small>type</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Abstraction100002137" href="http://dbpedia.org/class/yago/Abstraction100002137"><small>yago</small>:Abstraction100002137</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Cognition100023271" href="http://dbpedia.org/class/yago/Cognition100023271"><small>yago</small>:Cognition100023271</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Content105809192" href="http://dbpedia.org/class/yago/Content105809192"><small>yago</small>:Content105809192</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Idea105833840" href="http://dbpedia.org/class/yago/Idea105833840"><small>yago</small>:Idea105833840</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Ideal105923696" href="http://dbpedia.org/class/yago/Ideal105923696"><small>yago</small>:Ideal105923696</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/PsychologicalFeature100023100" href="http://dbpedia.org/class/yago/PsychologicalFeature100023100"><small>yago</small>:PsychologicalFeature100023100</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/ontology/ProgrammingLanguage" href="http://dbpedia.org/ontology/ProgrammingLanguage"><small>dbo</small>:ProgrammingLanguage</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatPrimeIdeals" href="http://dbpedia.org/class/yago/WikicatPrimeIdeals"><small>yago</small>:WikicatPrimeIdeals</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ca" >En matemàtiques, un ideal primer és un conjunt inclòs en un anell que té unes propietats semblants a les que tenen els nombres primers dins l'anell dels nombres enters. El concepte d'ideal primer té important rellevància, no només dins la pròpia teoria d'anells de l'àlgebra abstracta sinó també en teoria algebraica de nombres i en l'aritmètica modular.</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="cs" >Prvoideálem v okruhu je každý takový vlastní ideál , že pro libovolné dva ideály splňující (tedy jejichž součin je podmnožinou ) platí buď nebo . Jedná se o analogii prvočísel, u kterých lze obdobně vyslovit: Přirozené číslo je prvočíslem právě tehdy, pokud pro jakákoliv dvě přirozená čísla platí, že pokud dělí , pak buď dělí nebo dělí .</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >In der Ringtheorie ist ein Primideal eine Teilmenge eines Ringes, die sich ähnlich wie eine Primzahl als Element der ganzen Zahlen verhält.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="eo" >En ringo-teorio, prima idealo estas ĝeneraligo de la koncepto de primoj: ĝi estas tia idealo en komuta ringo, ke se iu produto apartenas al ĝi, tiam almenaŭ unu el la multiplikatoj apartenas al ĝi. En algebra geometrio, prima idealo respondas al punktoj en afinaj skemoj.</span><small> (eo)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >En la teoría de los anillos, una rama de la álgebra abstracta, el concepto de ideal primo es una generalización importante del concepto de número primo. Un ideal primo es un Ideal de un anillo conmutativo o no-conmutativo. Los ideales primos tienen una descripción más sencilla para los anillos conmutativos, por lo que distinguiremos los dos casos abajo.</span><small> (es)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >En algèbre commutative, un idéal premier d'un anneau commutatif unitaire est un idéal tel que le quotient de l'anneau par cet idéal est un anneau intègre. Ce concept généralise la notion de nombre premier à des anneaux à la structure moins simple d'accès que l'anneau des entiers relatifs. Ils jouent un rôle particulièrement important en théorie algébrique des nombres.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >素イデアル（英: prime ideal）は、環のイデアルで、ある条件を満たすものである。歴史的には、素数（素元）の概念の拡張としてデデキントによって代数体の整数環に対して定義された。整数環（一般にデデキント環）のすべてのゼロでない（整）イデアルは、素イデアルの有限個の積として（順序を除いて）一意的に書ける（イデアル論の基本定理）。スキームの理論は、図形の上の関数の成す環から下の空間を構成するという idea がもとになっているが、その時に、その環の素イデアルひとつひとつが、下の空間の点に対応する。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >환론에서 소 아이디얼(素ideal, 영어: prime ideal)은 아이디얼 가운데 소수와 같은 성질을 갖는 것들이다. 가환환의 소 아이디얼은 대수기하학에서 아핀 스킴의 부분다양체에 대응하며, 아핀 스킴의 위상 공간의 한 점을 이룬다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="it" >In matematica, e precisamente nella teoria degli anelli, un ideale primo è un ideale che ha alcune proprietà che lo rendono simile ad un numero primo nell'anello degli interi. Sarà dapprima presentata la definizione in un anello commutativo, poiché in questo caso gli ideali primi hanno una caratterizzazione più semplice, poi la generalizzazione in un anello qualsiasi.</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="nl" >In de abstracte algebra, een deelgebied van de wiskunde, is het begrip priemideaal een veralgemening van zowel een priemgetal als een . Priemidealen zijn "ondeelbaar" in de zin dat ze niet geschreven kunnen worden als product van twee andere idealen. Tenzij uitdrukkelijk anders vermeld, gaat dit artikel over priemidealen in een commutatieve ring met eenheidselement 1 verschillend van nul.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Первичный идеал является обобщением понятия простого числа в кольце целых чисел на произвольные (некоммутативные) кольца. Понятие простого идеала является частным случаем этого понятия.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pt" >Em álgebra, um ideal primo é um subconjunto de um anel que tem várias propriedades em comum com as de um número primo do anel dos inteiros. Os ideais primos para os inteiros são os conjuntos que contém todos os múltiplos de um número primo dado, juntamente com o ideal nulo. Ideais primitivos são primos, e ideais primos são tanto primários quanto semiprimos.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="sv" >Ett primideal är ett ideal P ≠ R i en kommutativ ring R, sådant att: för alla a och b i R. Om ringen R inte är kommutativ är P ett primideal, om det är ett äkta ideal och om det för ideal och sådana att gäller att antingen eller .</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >В абстрактній алгебрі простий ідеал — ідеал кільця, властивості якого схожі з властивостями простих чисел. Окрім теорії кілець поняття також часто використовується у алгебраїчній геометрії, де прості ідеали многочленів визначають афінні многовиди. Узагальненням поняття простого ідеала є примарний ідеал.</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >在数学中，素理想（Prime ideal）是环的一个子集，与整数环中的素数共享许多重要的性质。</span><small> (zh)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Ideał pierwszy – taki ideał właściwy pierścienia przemiennego z jedynką, dla którego z należenia do niego iloczynu dwóch danych elementów pierścienia wynika przynależność do niego choć jednego z czynników, tzn. ideał pierścienia nazywany jest pierwszym, gdy z należenia wynika, że lub Ideały pierwsze to w pewnym sensie te ideały, dla których zachodzi teza lematu Euklidesa o podzielności liczb całkowitych, tzn. odgrywają one rolę liczb pierwszych w teorii pierścieni. Pojęcie ideału pierwszego znajduje zastosowania w geometrii algebraicznej i teorii liczb.</span><small> (pl)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ca" >Ideal primer</span><small> (ca)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="cs" >Prvoideál (teorie okruhů)</span><small> (cs)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="de" >Primideal</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="eo" >Prima idealo</span><small> (eo)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="es" >Ideal primo</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Idéal premier</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="it" >Ideale primo</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >소 아이디얼</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >素イデアル</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="nl" >Priemideaal</span><small> (nl)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Prime ideal</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pl" >Ideał pierwszy (teoria pierścieni)</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pt" >Ideal primo</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="sv" >Primideal</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ru" >Первичный идеал (алгебра)</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="uk" >Простий ідеал</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="zh" >素理想</span><small> (zh)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.0677z" 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