This article is cited in 2 papers

Semigroup Varieties on Whose Free Objects Almost All Fully Invariant Congruences are Weakly Permutable

B. M. Vernikov

Ural State University

Abstract: A semigroup variety is said to be of index $\leqslant2$ if all nil-semigroups of the variety are semigroups with zero multiplication. We describe all semigroup varieties $\mathcal V$ of index $\leqslant2$ on free objects of which every two fully invariant congruences contained in the least semilattice congruence are weakly permutable, and semigroup varieties of index $\leqslant2$ all of whose subvarieties share the above-mentioned property.

Keywords: semigroup variety, nil-semigroup, weakly permutable congruence, fully invariant congruence.

UDC: 512.532.2

Received: 18.11.2003

 English version: Algebra and Logic, 2004, 43:6, 357–364

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