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A Characterization of Finitely Decidable Congruence Modular Varieties


Author: Pawel M. Idziak
Journal: Trans. Amer. Math. Soc. 349 (1997), 903-934
MSC (1991): Primary 03B25, 08A05; Secondary 03C13, 08B10, 08B26
DOI: https://doi.org/10.1090/S0002-9947-97-01904-1
MathSciNet review: 1407702
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Abstract: For every finitely generated, congruence modular variety $\mathcal {V}$ of finite type we find a finite family $\cal R$ of finite rings such that the variety $\mathcal {V} $ is finitely decidable if and only if $\mathcal {V}$ is congruence permutable and residually small, all solvable congruences in finite algebras from $\mathcal {V}$ are Abelian, each congruence above the centralizer of the monolith of a subdirectly irreducible algebra $\mathbf {A}$ from $\mathcal {V}$ is comparable with all congruences of $\mathbf {A}$, each homomorphic image of a subdirectly irreducible algebra with a non-Abelian monolith has a non-Abelian monolith, and, for each ring $R$ from $\cal R$, the variety of $R$-modules is finitely decidable.


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Additional Information

Pawel M. Idziak
Affiliation: Computer Science Department, Jagiellonian University, Kraków, Poland
Email: idziak@ii.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9947-97-01904-1
Keywords: Finite decidability, structure theory, congruence modularity
Received by editor(s): January 26, 1993
Received by editor(s) in revised form: January 15, 1994
Additional Notes: Research partially supported by KBN Grant No. 2 P301-029-04 and Fulbright Grant No. 17381.
Article copyright: © Copyright 1997 American Mathematical Society

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