Finitely decidable congruence modular varieties
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- by Joohee Jeong
- Trans. Amer. Math. Soc. 339 (1993), 623-642
- DOI: https://doi.org/10.1090/S0002-9947-1993-1150016-6
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Abstract:
A class $\mathcal {V}$ of algebras of the same type is said to be finitely decidable iff the first order theory of the class of finite members of $\mathcal {V}$ is decidable. Let $\mathcal {V}$ be a congruence modular variety. In this paper we prove that if $\mathcal {V}$ is finitely decidable, then the following hold. (1) Each finitely generated subvariety of $\mathcal {V}$ has a finite bound on the cardinality of its subdirectly irreducible members. (2) Solvable congruences in any locally finite member of $\mathcal {V}$ are abelian. In addition we obtain various necessary conditions on the congruence lattices of finite subdirectly irreducible algebras in $\mathcal {V}$.References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 339 (1993), 623-642
- MSC: Primary 08B10; Secondary 03B25
- DOI: https://doi.org/10.1090/S0002-9947-1993-1150016-6
- MathSciNet review: 1150016