We show that for a discrete semigroup S there exists a uniquely determined complete Boolean algebra B(S) the algebra of clopen subsets of M(S). M(S) is the phase space of the universal minimal dynamical system for S and it is an extremally disconnected compact Hausdorff space. We deal with this connection of semigroups and complete Boolean algebras focusing on structural properties of these alg...

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical ring flat algebra. In this paper, we show arithmetic and set-theoretic an equi-gcd

This work is about symmetric numerical semigroups. The semigroups are very important in semigroup theory. They play an role especially algebraic geometry, coding theory and other areas of algebra. Here, we examine Arf closure $S_q$ semigroup, give some relations between such that $S_q=\langle p, p q+k\rangle$, where $p$ a prime number $q \geq 1, q \in \mathbb{Z}$ for $k=1,2$ $p-1$. Received: Ju...

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on the intersection lattice of the hyperplane arrangement. A complete systemof primitive orthogonal idempotents for the algebra is constructed and other algebr...

We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson’s concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced C∗-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing t...

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach algebraM(βS...

We study the relation (and differences) between stability and Property (S) in simple stably finite framework. This leads us to characterize stable elements terms of their support, these concepts from different sides: hereditary subalgebras, projections multiplier algebra order properties Cuntz semigroup. use approaches show both that cancellation at infinity on semigroup just holds when its equ...