Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

Cancellative semigroups with non-empty center

Abstract: Cancellative, idempotent-free semigroups having non-empty center are characterized in terms of a Schreier extension Cancellative pivoted semigroups with non-empty center are characterized as a group or in terms of a triple (G,H,I), where G is a group, H is either empty or a subgroup of G and I is a function mapping GxG into the non negative integers

The universal nilpotent group compactification of a semigroup

Abstract: The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group. The general approach to the theory of semigroup compactification is based on the Gelfand-Naimark theory of C∗-algebras of functions. There are many papers which deal with the characterization of certain universal semigroup compactifications in terms of function algebras. Seminal work in this context was done by K. de Leeuw and I. Glicksberg [3]. The universal group compactification is given by Junghenn [6], in terms of some types of distal functions. This paper deals with the construction of a function algebra on a semitopological semigroup, used to characterize the universal nilpotent group compactification of it, and investigating some of its properties. First we recall some preliminaries. Throughout this paper, S shall be a semitopological semigroup, unless otherwise mentioned. For notation and terminology we shall follow Berglund et al. [2] as far as possible. Thus a semigroup compactification of S is a pair (ψ,X), where X is a compact, Hausdorff, right topological semigroup and ψ : S → X is a continuous homomorphism with dense image such that for each s ∈ S, the mapping x 7→ ψ(s)x : X → X is continuous. The C∗-algebra of all continuous bounded complex-valued functions on a topological space Y is denoted by C(Y ). For C(S) left and right translations Ls and Rt are defined for all s, t ∈ S and f ∈ C(S) by (Lsf)(t) = f(st) = (Rtf)(s). A left translation invariant C∗-subalgebra F of C(S) (i.e. Lsf ∈ F for all s ∈ S and f ∈ F ) containing the constant functions is called m-admissible if the function s 7→ (Tμf)(s) = μ(Lsf) is in F for all f ∈ F and μ ∈ S (=the spectrum of F ); then the product of μ, ν ∈ S can be defined by μν = μ ◦ Tν and the Gelfand topology on S makes ( , S ) a semigroup compactification (called the F -compactification) of S, where : S → S is the evaluation mapping. The reader is referred to sections 3.1 and 3.3 of [2] for the one-to-one correspondence between compactifications of S and m-admissible subalgebras of C(S), and also for a discussion of universal P -compactifications, whose existence for a wide variety of properties P is given in terms of subdirect products. Received by the editors January 16, 1996. 1991 Mathematics Subject Classification. Primary 22A20, 43A60.

The space of nodal curves of type p , q with given Weierstraß semigroup

Abstract: We continue the investigation of curves of type p, q started in Knebl et al. (J Algebra 348:315–335, 2011). We study the space of such curves and the space of nodal curves with prescribed Weierstras semigroup. A necessary and sufficient criterion for a numerical semigroup to be a Weierstras semigroup is given. Using this criterion we find a class of Weierstras semigroups which apparently has not yet been described in the literature.

On compact quantum semigroup QS red

Abstract: We study some properties of a reduced semigroup C*-algebra of a semigroup S. For the semigroup C*-algebra generated by the deformation of the algebra of continuous functions on a compact abelian group we obtain a structure of a compact quantum semigroup. We also consider morphisms of constructed compact quantum semigroups.

A weak 2-weight problem for the Poisson-Hermite semigroup

Abstract: This survey is a slightly extended version of the lecture given by the author at the VI International Course of Mathematical Analysis in Andalućıa (CIDAMA), in September 2014. Most results form part of the paper [3], written jointly with S. Hartzstein, T. Signes, J.L. Torrea and B. Viviani.