Group theory and semigroup theory have developed in somewhat different directions in the past several decades. While Cayley’s theorem enables us to view groups as groups of permutations of some set, the analogous result in semigroup theory represents semigroups as semigroups of functions from a set to itself. Of course both group theory and semigroup theory have developed significantly beyond t...

For any group G and any set A, a cellular automaton (CA) is a transformation of the configuration space A G defined via a finite memory set and a local function. Let CA(G; A) be the monoid of all CA over A G. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element τ ∈ CA(G; A) is von Neumann regular (or simply regular) if there ...

Regular semigroups and their structures are the most wonderful part of semigroup theory, contents very rich. In order to explore more regular semigroups, this paper extends relevant classical conclusions from a new perspective: by transforming positions elements in regularity conditions, some conditions (collectively referred as transposition regularity) obtained, concepts various introduced (L...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

Let R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R S is isomorphic to the direct product of Munn algebras M R GJ , mJ , nJ ;PJ with J ∈ S/J, where mJ is the number of R-classes in J , nJ the number of L-classes in J , and GJ a maximum subgroup of J . As applications, we obtain the sufficient and necessary conditions for the semigroup ...

Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-known random walks. For example, the set of faces of a hyperplane arrangement is endowed with a left regular band structure. This paper studies the module structure of the semigroup algebra of an arbitra...

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

Abstract Twisted étale groupoid algebras have recently been studied in the algebraic setting by several authors connection with an abstract theory of Cartan pairs rings. In this paper we show that extensions ample groupoids correspond a precise manner to Boolean inverse semigroups. particular, discrete twists over certain abelian semigroups, and they are classified Lausch’s second cohomology gr...

The author proves that, if S is an FIC-semigroup or a completely regular semigroup, and if RS is a ring with identity, then R < E(S) > is a ring with identity. Throughout this paper, R denotes as a ring with identity. Let S be a semigroup, X ⊆ S . The following notations are used in the paper: < X > : the subsemigroup of S generated by X ; |X| : the cardinal number of X ; E(S): the set of idemp...