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Zbl 0735.08001
Duda, J.
$A\times A$ congruence coherent implies $A$ congruence regular. (English)
[J] Algebra Univers. 28, No.2, 301-302 (1991). ISSN 0002-5240; ISSN 1420-8911/e

It has been known for a long time that any variety of congruence coherent algebras is congruence permutable and congruence regular [see {\it D. Geigher}, "Congruence coherent algebras", Preprint (1974)]. A local version of the first assertion was recently proved by {\it D. M. Clark} and {\it I. Fleischer} [Algebra Univers. 24, 192 (1987; Zbl 0634.08001)]. We show that the second implication can be sharpened in a similar way.

MSC 2000:: *08A30 Subalgebras of general algebraic systems
08B10 Congruence modularity and generalizations in varieties of algebras

Keywords: congruence permutable variety; congruence regular variety; congruence coherent algebras

Citations: Zbl 0634.08001

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