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Finite equational bases for congruence modular varieties

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Abstract

In this paper it is proved that a variety generated by a finite algebraic system with finitely many operations is finitely axiomatizable, provided that the variety is congruence modular and residually small. This result is an extension to congruence modular varieties of a well known theorem for congruence distributive varieties, due to K. A. Baker. Also, under somewhat less restrictive hypotheses, (which are satisfied by finite groups and rings) it is proved that a finite algebraic system belongs to a finitely axiomatizable locally finite variety.

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Research supported by National Science Foundation Grant No. DMS-8302295.

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McKenzie, R. Finite equational bases for congruence modular varieties. Algebra Universalis 24, 224–250 (1987). https://doi.org/10.1007/BF01195263

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