Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

Central subsets of a discrete semigroup S have very strong combinatorial properties which are a consequence of the Central Sets Theorem. Call a set a C-set if it satisfies the conclusion of the Central Sets Theorem. We obtain here a reasonably simple characterization of C-sets in an arbitrary discrete semigroup.

We formulate the dynamics of an infinitely extended open dissipative quantum system , Σ, in Schroedinger picture. The generic model on which this is based comprises a C★-algebra, A observables, folium, ℱ states algebra and one-parameter semigroup, τ linear transformations that represents its given by natural infinite-volume limit corresponding semigroup for finite system. On basis, we establish...

In this paper we study complex representations of the factorpower FP(G,M) of a finite group G acting on a finite set M . This includes the finite monoid FP+(Sn), which can be seen as a kind of a “balanced” generalization of the symmetric group Sn inside the semigroup of all binary relations. We describe all irreducible representations of FP(G,M) and relate them to irreducible representations of...

We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family inner products, also providing new information on order extreme points in some previously studied cases.

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals coefficients in factorizations semigroup elements. This work generalizes many previous results, provides more natural and intuitive proofs, yields a completely explicit error bound.

A generalization of the original Diffie-Hellman key exchange in (Z/pZ) found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build in...