Topic
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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01 Jun 2014
TL;DR: In this paper, the full and reduced C *-algebras of I l (S) are related to Li's C * -algesia, and conditions for their isomorphicity are given.
Abstract: To each discrete left cancellative semigroup S one may associate an inverse semigroup I l (S) , often called the left inverse hull of S . We show how the full and reduced C *-algebras of I l (S) are related to the full and reduced semigroup C *-algebras for S , recently introduced by Li, and give conditions ensuring that these algebras are isomorphic. Our picture provides an enhanced understanding of Li's algebras.
47 citations
TL;DR: Theorem 1.3 as mentioned in this paper shows that any proper inverse semigroup P can be embedded in a semidirect product P of a semilattice and a group, where P is bisimple with identity.
46 citations
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45 citations
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TL;DR: In this article, the authors extend the usual ring concept to the case where the underlying group and semigroup are respectively ann-ary group and anm-ary semigroup, and they apply it to homomorphism theorems.
Abstract: The following paper is concerned with the extension of the usual ring concept to the case where the underlying group and semigroup are respectively ann-ary group and anm-ary semigroup. Most attention has been paid to homomorphism theorems and to some idealtheoretic aspects.
45 citations
TL;DR: On the infinite semigroup of matrix units, there exists no semigroup compact [countably compact] topology, and any continuous homomorphism from the infinite topological matrix units into a compact topological semigroup is annihilating.
Abstract: On the infinite semigroup of matrix units there exists no semigroup compact [countably compact] topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically h-closed in the class of topological inverse semigroups. Some H-closed minimal semigroup topologies on the infinite semigroup of matrix units are considered.
44 citations