Volkov, M. V. 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. Reviewer: G.Pollák (Szeged) Cited in 2 Documents 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 Keywords:varieties of semigroups; fully invariant congruences; free semigroups; distributive lattice of subvarieties Citations:Zbl 0745.00034 PDFBibTeX XMLCite \textit{M. V. Volkov}, Contemp. Math. 131, 295--316 (1992; Zbl 0768.20025)