M-Strongly Solid Subvarieties of Some Varieties of Commutative Semigroups

摘要

A generalized hypersubstitution of type τ maps any operation symbols to the set of all terms of the same type which does not necessarily preserve the arity. The extensions of generalized hypersubstitutions are mappings on the set of all terms. A binary operation on the set of all generalized hypersubstitutions is defined by using this extension. It turns out that this set with the binary operation forms a monoid. In this paper, we studyM-strongly solid subvarieties of commutative nilpotent semigroups and M-strongly solid subvarieties of commutative semigroups which satisfies x_0x_1 . . . x_k ≈ y_0y_1 . . . y_k for any natural number k.