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Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: The theory of inverse semigroups as discussed by the authors is a refinement of the Wagner-Preston representation theorem, which states that every inverse semigroup is isomorphic to an inverse monoid of some structure.
31 citations
31 citations
TL;DR: In this paper, the uniqueness or non-uniqueness of these factorizations is measured in terms of the uniqueness of factorizations in the integral domain of the cancellative semigroup of upper triangular matrices.
31 citations
TL;DR: In this paper, the essential and absolutely continuous spectra do not change when one adds an extra Dirichlet boundary condition on a "small" set, and the corresponding semigroup differences are Hilbert-Schmidt or trace class.
31 citations
TL;DR: Extensions of semigroups have been studied from two points of view; ideal extensions and Schreier extension as mentioned in this paper. But the main result of Theorem 2 is stated in the form of the classical treatment of SchReier extensions (see e.g.
Abstract: Extensions of semigroups have been studied from two points of view; ideal extensions and Schreier extension. In this paper another type of extension is considered for the class of inverse semigroups. The main result (Theorem 2) is stated in the form of the classical treatment of Schreier extensions (see e.g.[7]). The motivation for the definition of idempotentseparating extension comes primarily from G. B. Preston's concept of a normal set of subsets of a semigroup [6]. The characterization of such extensions is applied to give another description of bisimple inverse ω-semigroups, which were first described by N. R. Reilly [8]. The main tool used in the proof of Theorem 2 is Preston's characterization of congruences on an inverse semigroup [5]. For the standard terminology used, the reader is referred to [1].
31 citations