Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.

Endomorphisms of , , and

Abstract: We describe all endomorphisms of the (finite) Brauer semigroup, its partial analogue and the semigroup of all partitions of a -element set.

Profinite methods in semigroup theory

Abstract: Many recent results in finite semigroup theory make use of profinite methods, that is, they rely on the study of certain infinite, compact semigroups which arise as projective limits of finite semigroups. These ideas were introduced in semigroup theory in the 1980s, first to describe pseudovarieties in terms of so-called pseudo-identities: this is Reiterman's theorem, which can be viewed as the (much more complex) finite algebra analogue of Birkhoff's variety theorem. Soon, these methods were used in conjunction with virtually all the other approaches of finite semigroups, notably to study the decidability of product pseudovarieties. This paper surveys the contribution of profinite methods and the way they enriched and modified finite semigroup theory.

Normal forms for free aperiodic semigroups

Abstract: The implicit operation ω is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates Using ω there is a well-defined algebra which is known as the free aperiodic semigroup In this article we introduce a specific and rather elementary list of pseudoidentitites, we show that for each n, the n-generated free aperiodic semigroup is defined by this list of pseudoidentities, and then we use this identification to show that it has a decidable word problem In the language of implicit operations, this shows that the pseudovariety of finite aperiodic semigroups is κ-recursive This completes a crucial step towards showing that the Krohn–Rhodes complexity of every finite semigroup is decidable