Bases of identities of varieties of lattice ordered semigroups
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.
scientific article; zbMATH DE number 3861226