<?xml version="1.0" encoding="utf-8"?> <feed xmlns="http://www.w3.org/2005/Atom"> <title type="text">Recent zbMATH articles in MSC 08B05</title> <id>https://zbmath.org/atom/cc/08B05</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/" /> <link href="https://zbmath.org/atom/cc/08B05" rel="self" /> <generator>Werkzeug</generator> <entry xml:base="https://zbmath.org/atom/cc/08B05"> <title type="text">Varieties of quantitative algebras and their monads</title> <id>https://zbmath.org/1553.08008</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/1553.08008" /> <author> <name>"Adamek, Jiri"</name> <uri>https://zbmath.org/authors/?q=ai:adamek.jiri</uri> </author> </entry> <entry xml:base="https://zbmath.org/atom/cc/08B05"> <title type="text">Fixed-points for quantitative equational logics</title> <id>https://zbmath.org/1553.08014</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/1553.08014" /> <author> <name>"Mardare, Radu"</name> <uri>https://zbmath.org/authors/?q=ai:mardare.radu</uri> </author> <author> <name>"Panangaden, Prakash"</name> <uri>https://zbmath.org/authors/?q=ai:panangaden.prakash</uri> </author> <author> <name>"Plotkin, Gordon"</name> <uri>https://zbmath.org/authors/?q=ai:plotkin.gordon-d</uri> </author> </entry> <entry xml:base="https://zbmath.org/atom/cc/08B05"> <title type="text">Beyond nonexpansive operations in quantitative algebraic reasoning</title> <id>https://zbmath.org/1553.08015</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/1553.08015" /> <author> <name>"Mio, Matteo"</name> <uri>https://zbmath.org/authors/?q=ai:mio.matteo</uri> </author> <author> <name>"Sarkis, Ralph"</name> <uri>https://zbmath.org/authors/?q=ai:sarkis.ralph</uri> </author> <author> <name>"Vignudelli, Valeria"</name> <uri>https://zbmath.org/authors/?q=ai:vignudelli.valeria</uri> </author> </entry> <entry xml:base="https://zbmath.org/atom/cc/08B05"> <title type="text">Algebras from finite group actions and a question of Eilenberg and Sch眉tzenberger</title> <id>https://zbmath.org/1553.08016</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/1553.08016" /> <author> <name>"Shaheen, Salma"</name> <uri>https://zbmath.org/authors/?q=ai:shaheen.salma</uri> </author> <author> <name>"Willard, Ross"</name> <uri>https://zbmath.org/authors/?q=ai:willard.ross</uri> </author> <content type="text">Summary: In 1976 \textit{S. Eilenberg} and \textit{M. P. Sch眉tzenberger} [Adv. Math. 19, 413--418 (1976; Zbl 0351.20035)] posed the following diabolical question: if \textbf{A} is a finite algebraic structure, \(\Sigma\) is the set of all identities true in \textbf{A}, and there exists a finite subset \(F\) of \(\Sigma\) such that \(F\) and \(\Sigma\) have exactly the same \textit{finite} models, must there also exist a finite subset \(F'\) of \(\Sigma\) such that \(F'\) and \(\Sigma\) have exactly the same \textit{finite and infinite} models? (That is, must the identities of \textbf{A} be ``finitely based''?) It is known that any counter-example to their question (if one exists) must fail to be finitely based in a particularly strange way. In this paper we show that the ``inherently nonfinitely based'' algebras constructed by Lawrence and Willard from group actions do \textit{not} fail to be finitely based in this particularly strange way, and so do not provide a counter-example to the question of Eilenberg and Sch眉tzenberger [loc. cit.]. As a corollary, we give the first known examples of inherently nonfinitely based ``automatic algebras'' constructed from group actions.</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/08B05"> <title type="text">Lattices of varieties of plactic-like monoids</title> <id>https://zbmath.org/1553.20162</id> <updated>2025-04-04T17:10:03.436181Z</updated> <link href="https://zbmath.org/1553.20162" /> <author> <name>"Aird, Thomas"</name> <uri>https://zbmath.org/authors/?q=ai:aird.thomas</uri> </author> <author> <name>"Ribeiro, Duarte"</name> <uri>https://zbmath.org/authors/?q=ai:ribeiro.duarte</uri> </author> <content type="text">Summary: We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the axiomatic ranks of their elements, obtain plactic-like congruences whose corresponding factor monoids generate varieties in the lattice, and determine which varieties are joins of the variety of commutative monoids and a finitely generated variety. We also show that the hyposylvester and metasylvester monoids generate the same variety as the sylvester monoid.</content> </entry> </feed>

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