Finitely decidable congruence modular varieties

Author:
Joohee Jeong

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

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Abstract: A class of algebras of the same type is said to be *finitely decidable* iff the first order theory of the class of finite members of is decidable. Let be a congruence modular variety. In this paper we prove that if is finitely decidable, then the following hold. (1) Each finitely generated subvariety of has a finite bound on the cardinality of its subdirectly irreducible members. (2) Solvable congruences in any locally finite member of are abelian. In addition we obtain various necessary conditions on the congruence lattices of finite subdirectly irreducible algebras in .

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DOI:
https://doi.org/10.1090/S0002-9947-1993-1150016-6

Article copyright:
© Copyright 1993
American Mathematical Society