Document Zbl 0984.00001

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The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/lang.serge" title="Author Profile">Lang, Serge</a></div> <h2 class="title"> <strong>Algebra. 3rd revised ed.</strong> <i>(English)</i> <a class="label nowrap" href="/0984.00001">Zbl 0984.00001</a> </h2> <div class="source"> <a href="/serials/3917" title="Series Profile">Graduate Texts in Mathematics</a>. 211. New York, NY: Springer. xv, 914 p. (2002). </div> <div class="abstract">The first edition of this book (1965; <a href="/0193.34701">Zbl 0193.34701</a>) consisted of three parts: basic concepts, field theory and linear algebra, and as a modern down-to-earth approach with a personal touch it attained great popularity. The second edition (1984; <a href="/0712.00001">Zbl 0712.00001</a>) added some topics, mainly on commutative algebra and homological algebra.<br class="zbmathjax-paragraph">The current third edition has grown again, the additions dealing with topics close to the author’s heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields: Bernoulli numbers, Fermat’s last theorem for polynomials, the Gelfond-Schneider theorem and (as an exercise, with a hint) the Iss’sa-Hironaka theorem. This makes it a fascinating book to read, but despite its length it leaves large parts of algebra untouched. Semisimple algebras get a very cursory treatment (no mention of crossed products or the Brauer group) and there is only the merest trace of Morita theory; there are no Ore domains, Goldie theory or PI-theory. Graphs, linear programming and codes, constructions like ultraproducts and Boolean algebras are also absent, and lattices are only of the number-theoretic sort (reseaux, not treillis).<br class="zbmathjax-paragraph">Bearing these limitations in mind, the reader will nevertheless find a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items.<br class="zbmathjax-paragraph">Editorial comment: Note that there is also a 3rd ed. published by Addison-Wesley 1993 reviewed in <a href="/0848.13001">Zbl 0848.13001</a>.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A294">Paul M.Cohn (London)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A1703931">Cited in <strong>18</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A1703931">Cited in <strong>1025</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A00A05" title="MSC2020">00A05</a> </td> <td class="space"> Mathematics in general </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A12-01" title="MSC2020">12-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A13-01" title="MSC2020">13-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15-01" title="MSC2020">15-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A16-01" title="MSC2020">16-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A18-01" title="MSC2020">18-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A20-01" title="MSC2020">20-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A14-01" title="MSC2020">14-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A11-01" title="MSC2020">11-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aalgebra">algebra</a>; <a href="/?q=ut%3Amodules">modules</a>; <a href="/?q=ut%3Afields">fields</a>; <a href="/?q=ut%3Acomplexes">complexes</a>; <a href="/?q=ut%3Agroups">groups</a>; <a href="/?q=ut%3Acommutative+algebra">commutative algebra</a>; <a href="/?q=ut%3Ahomological+algebra">homological algebra</a>; <a href="/?q=ut%3Aalgebraic+geometry">algebraic geometry</a>; <a href="/?q=ut%3Afunction+theory">function theory</a>; <a href="/?q=ut%3Anumber+theory">number theory</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0712.00001">Zbl 0712.00001</a>; <a href="/0193.34701">Zbl 0193.34701</a>; <a href="/0848.13001">Zbl 0848.13001</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0984.00001" data-ciurl="/ci/01703931" data-biburl="/bibtex/01703931.bib" data-amsurl="/amsrefs/01703931.bib" data-xmlurl="/xml/01703931.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01703931.pdf" title="Zbl 0984.00001 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </div> </div> </article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2024 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; 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