Let S-Top be the category of topological S-acts over a topological semigroup S and S-SemiTop be the category of semitopological S-acts over a semitopological semigroup S. It is obvious that any topological S-act is a semitopological S-act, however we will see that the converse is not true in general. In this note, we study the universal objects in the category of semitopological S-acts and intr...

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

This paper concerns the structure of strongly continuous one parameter semigroups of completely positive contractions of B(H) = B(K⊗L(0,∞)) which are intertwined by translation. These are called CP -flows over K. Using Bhat’s dilation result each unital CP -flow over K dilates to an Eo-semigroup of B(H1) where H1 can be considered to contain B(K⊗L(0,∞)). Every spatial Eo-semigroup is cocycle co...

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...

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...

Simon (Theoret. Comput. Sci. 72 (1990) 65–94) has proved that every morphism from a free semigroup to a $nite semigroup S admits a Ramseyan factorization forest of height at most 9|S|. In this paper, we prove the same result of Simon with an improved bound of 7|S|. We provide a simple algorithm for constructing a factorization forest. In addition, we show that the algorithm cannot be improved s...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

A way of utilizing Lax-Phillips type semigroups for the description of time evolution of resonances for scattering problems involving Hamiltonians with a semibounded spectrum was recently introduced by Y. Strauss. In the proposed framework the evolution is decomposed into a background term and an exponentially decaying resonance term evolving according to a semigroup law given by a Lax-Phillips...

Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: (i) for many simple C∗-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott’s classification theorem for simple, unital AI algebras; (ii) for the algebras in (i), classification of their Hilbert modules is similar to the von Neu...

This note shows how iteration of the standard process of adjoining identities and zeros to semigroups gives rise naturally to the lexicographical ordering on the additive semigroups of n-tuples of nonnegative integers and n-tuples of integers. 1. Semigroups with identities and zeros A binary operation ∗ on a set S is associative if (a ∗ b) ∗ c = a ∗ (b ∗ c) for all a, b, c ∈ S. A semigroup is a...