Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization. 1...

This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

Let S be a semigroup and K be a field. A K-space K[S], with basis S and with multiplication extending, in a natural way, the operation on S, is called a semigroup algebra. It remains an open problem to characterize semigroup algebras that are a prime Noetherian maximal order. In this thesis, we give an answer to the problem for a large class of cancellative semigroups and we illustrate these re...

We introduce a new class of noncommutative rings-Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Galois orders generalizes classical orders in noncommutative rings and contains many classical objects, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, assoc...