Narrow Results

This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B₂, denoted V*(B₂). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B₂ which leads to the main result, which states that V*(B₂) is decidable.

Independently, using some suggestions given by J. Almeida in his book "Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in V* (B₂).

Using purely syntactical arguments, it is shown that every nontrivial pseudovariety of monoids contained in DO whose corresponding variety of languages is closed under unambiguous product, for instance DA, is local in the sense of Tilson.

We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite pro-identity basis for the pseudovariety of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.