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Pondělíček, Bedřich

Tolerance distributive and tolerance modular varieties of commutative semigroups. (English) Zbl 0614.20043

Czech. Math. J. 36(111), 485-488 (1986).
A “tolerance” on a semigroup \(S\) is a reflexive and symmetric subsemigroup of \(S\times S\). The author proves the following theorem: a variety \(V\) of commutative semigroups is tolerance modular, that is, each member of \(V\) has modular lattice of tolerances, if and only if \(V\) satisfies an identity \(xy=xyz^ n\) for some positive integer n. Further, amongst such varieties, only the variety of “zero”, or “null”, semigroups and the trivial variety are tolerance distributive.
Reviewer: P.R.Jones

Cited in 3 Documents

MSC:

20M07 Varieties and pseudovarieties of semigroups
08A30 Subalgebras, congruence relations
08B10 Congruence modularity, congruence distributivity
20M14 Commutative semigroups

Keywords:

variety of commutative semigroups; tolerance modular; modular lattice of tolerances; tolerance distributive
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\textit{B. Pondělíček}, Czech. Math. J. 36(111), 485--488 (1986; Zbl 0614.20043)
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References:

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