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Congruence semimodular varieties I: Locally finite varieties [PDF]

Algebra Universalis, 1994
[Part II is reviewed below.] The authors try to answer the question: How much of the structure involved in congruence modular varieties exists for congruence semimodular (CSM) varieties? They examine locally finite CSM varieties. For any finite algebra \(A\) in a CSM variety, natural congruences \(\underset {T}\sim\) are defined which play a role ...
AGLIANO', PAOLO, Kearnes, K.
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ON LOCAL FINITENESS IN VARIETIES OF ASSOCIATIVE ALGEBRAS

Mathematics of the USSR-Sbornik, 1982
A variety of algebras is called distinguished if there is a countably generated, locally finite algebra such that any other countably generated locally finite algebra is a homomorphic image of . This article continues the investigation of the question of when a variety of associative algebras is distinguished.For example, if the ground field is ...
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Applications of Finite Duality to Locally Finite Varieties of BL-Algebras

2008
We are concerned with the subvariety of commutative, bounded, and integral residuated lattices, satisfying divisibility and prelinearity, namely, BL-algebras. We give an explicit combinatorial description of the category that is dual to finite BL-algebras. Building on this, we obtain detailed structural information on the locally finite subvarieties of
S. Aguzzoli, S. Bova, V. Marra
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Homogeneous locally finite varieties

Algebra Universalis, 1992
A locally finite variety is said to be homogeneous if every isomorphism between subalgebras of a finite algebra in the variety extends to an automorphism of the algebra. The author proves the following claim: every homogeneous locally finite variety of finite type is finitely axiomatizable.
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On locally finite varieties with undecidable equational theory

Algebra Universalis, 2002
A variety \(\mathcal V\) is pseudorecursive if every finitely generated \(\mathcal V\)-free algebra has a decidable word problem but the equational theory of \(\mathcal V\) is undecidable. It is known that undecidability of the equational theory implies the undecidability of the uniform word problem.
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Locally finite varieties with large free spectra

Algebra Universalis, 2002
For a variety \(\mathcal V\), \(f_{\mathcal V}(n)\) denotes the size of the free algebra on \(n\) generators in \(\mathcal V\) and \(g_{\mathcal V}(n)\) is the number of non-isomorphic algebras in \(\mathcal V\) generated by \(n\) or fewer elements. Thus \(\mathcal V\) is locally finite if \(f_{\mathcal V}(n)\) is an integer for any positive integer ...
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ON THE ORDERS OF FREE GROUPS OF LOCALLY FINITE VARIETIES

Mathematics of the USSR-Izvestiya, 1973
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VARIETIES IN REPRESENTATIONS OF FINITE GROUPS. LOCALLY STABLE VARIETIES. MATRIX GROUPS AND VARIETIES OF REPRESENTATIONS

Russian Mathematical Surveys, 1979
ContentsIntroductionChapter 1. Stability § 1. Identities of stable varieties § 2. Locally stable and unipotent varieties § 3. The algebra of stable varieties § 4. Classification questions for stable varieties § 5. Magnus varieties of representationsChapter 2. Locally finite and locally bounded varieties § 1. Locally bounded varieties § 2.
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Congruence meet-semidistributive locally finite varieties and a finite basis theorem

Algebra universalis, 2018
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McNulty, George F., Willard, Ross
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ON THE LOCALLY FINITE p-GROUPS IN CERTAIN VARIETIES OF GROUPS

The Quarterly Journal of Mathematics, 1992
The famous result of \textit{E. I. Zel'manov} [Izv. Akad. Nauk. SSSR, Ser. Mat. 54, No. 1, 42-59 (1990; Zbl 0704.20030)], solving the restricted Burnside problem, combined with a result of Kovács, given in [\textit{H. Neumann}, Varieties of groups, Springer-Verlag (1967; Zbl 0251.20001)], shows that the class, \({\mathcal R}_{p^\lambda}\), of locally ...
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