Pseudovariety joins involving J -trivial semigroups and completely regular semigroups

Tameness of pseudovariety joins involving R 1

In this paper, we establish several decidability results for pseudovariety joins of the form V ∨ W, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp. R) denotes the pseudovariety of all J-trivial (resp. R-trivial) semigroups. In particular, we show that the pseudovariety V ∨ W is (completely) κ-tame when V is a subpseudovariety of J with decidable κ-word problem and W is...

Tameness of pseudovariety joins

The concept of tameness of a pseudovariety was introduced by Almeida and Steinberg [1] as a tool for proving decidability of the membership problem for semidirect products of pseudovarieties. Recall that the join V ∨ W of two pseudovarieties V and W is the least pseudovariety containing both V and W. This talk is concerned with the problem of proving tameness of joins. This problem was consider...

Reducibility of Pointlike Problems

We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of elements of a fixed set π of primes; the pseudovariety of all finite semigroups in which every regular J-class is the product of a rectangular band by a group from...

Decidability and Tameness in the Theory of Finite Semigroups

The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups

This article solves a problem proposed by Almeida: the computation of the join of two well-known pseudovarieties of semigroups, namely the pseudovariety of bands and the pseudovariety of locally trivial semigroups. We use a method developed by Almeida, based on the theory of implicit operations.