Bases of identities of varieties of lattice ordered semigroups
type: Item
instance of: scholarly article
title: Bases of identities of varieties of lattice ordered semigroups
zbMATH Open document ID: 0542.06006
DOI: 10.1007/BF01978878
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187249
review text: 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.
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3861226
zbMATH Keywords: lattice ordered semigroup
zbMATH Keywords: variety
zbMATH Keywords: commutative cancellative dld- semigroup
zbMATH Keywords: equational base
author: Vladimir B. Repnitskiǐ
MaRDI profile type: Publication
cites work: Sur les demi-groupes réticulés et les O-demi-groupes. (Lattice ordered semigroups and O-semigroups)
cites work: Primitive Satisfaction and Equational Problems for Lattices and Other Algebras
description: scientific article; zbMATH DE number 3861226