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\(A\times A\) congruence coherent implies \(A\) congruence regular. (English) Zbl 0735.08001
It has been known for a long time that any variety of congruence coherent algebras is congruence permutable and congruence regular [see D. Geigher, ”Congruence coherent algebras”, Preprint (1974)]. A local version of the first assertion was recently proved by D. M. Clark and I. Fleischer [Algebra Univers. 24, 192 (1987; Zbl 0634.08001)]. We show that the second implication can be sharpened in a similar way.

MSC:
08A30 Subalgebras, congruence relations
08B10 Congruence modularity, congruence distributivity
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[1] Clark, D. M. andFleischer, I.,A?A congruence coherent implies A congruence permutable. Algebra Univ.24 (1987), 192. · Zbl 0634.08001
[2] Geigher, D.,Congruence coherent algebras, 1974 Preprint; also see AMS Notices,21 (1974) A436.
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