×

Semigroup varieties with commuting fully invariant congruences on free objects. (English) Zbl 0768.20025

Algebra, Proc. Int. Conf. Memory A. I. Mal’cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 3, 295-316 (1992).
[For the entire collection see Zbl 0745.00034.]
All varieties of semigroups such that the fully invariant congruences of their free semigroups commute are described. This also makes possible a slight improvement of the author’s and Vernikov’s description of semigroup varieties with distributive lattice of subvarieties.

MSC:

20M07 Varieties and pseudovarieties of semigroups
08B10 Congruence modularity, congruence distributivity
20M15 Mappings of semigroups
08B15 Lattices of varieties
20M05 Free semigroups, generators and relations, word problems

Citations:

Zbl 0745.00034
PDFBibTeX XMLCite