Profinite semigroups may be described briefly as projective limits of finite semigroups. They
come about naturally by studying pseudovarieties of finite semigroups which in turn serve as …

In algebraic terms, the insertion of n-powers in words may be modelled at the language level
by considering the pseudovariety of ordered monoids defined by the inequality 1⩽ xn. We …

A Note on the Equation PH = JH Page 1 A Note on the Equation PH = JH Benjamin Steinberg
January 14, 1999 Abstract This note shows that PH = H = JH = Jm H holds for any non-trivial …

We characterize aperiodic relational morphisms as those that are injective on regular \H-
classes. This result is applied to obtain simple proofs and generalizations of McAlister's …

This paper gives a proof, using geometric techniques, of the theorem of Henckell and
Rhodes that J* G= Jⓜ G, a key ingredient of the proof that PG= BG. The purpose of this …

We show that if S is a finite semigroup with aperiodic idempotent-generated subsemigroup
and H is a pseudovariety of groups, then the sequence of iterated H-kernels of S stops at the …

The purpose of this paper is to contribute to the theory of profinite semigroups by
considering the special class consisting of those all of whose finitely generated closed …

The notion of Abelian kernel of a finite monoid extends the notion of derived subgroup of a
finite group. In this line, an extension of the notion of solvable group to monoids is quite …

Nilpotent semigroups in the sense of Mal'cev are defined by semigroup identities. Finite
nilpotent semigroups constitute a pseudovariety, MN, which has finite rank. The semigroup …

This is the first part of a series of three papers in which we show that certain important
classes of regular semigroups admit no finite basis for their quasiidentities and …