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Bases of identities of varieties of lattice ordered semigroups. (English. Russian original) Zbl 0542.06006

Algebra Logic 22, 461-472 (1983); translation from Algebra Logika 22, No. 6, 649-665 (1983).
The author calls a lattice ordered semigroup S a dld-semigroup, if S is distributive as a lattice and satisfies the identities \(x(y\wedge z)=(xy)\wedge(xz),\quad(x\wedge y)z=(xz)\wedge(yz).\) The following result is proved. The variety generated by any nontrivial commutative cancellative dld-semigroup is not finitely based. Also, an equational base for the variety generated by an infinite cyclic group and for the variety generated by an infinite cyclic semigroup (both ordered naturally) is found.
Reviewer: V.Novák

MSC:

06F05 Ordered semigroups and monoids
08B05 Equational logic, Mal’tsev conditions
06B20 Varieties of lattices
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References:

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