Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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Journal Article•
8 citations
TL;DR: In this article, the authors studied the number of nonzero irreducible modular representations of a semigroup S by matrices over an algebraically closed field of non-zero characteristic.
Abstract: In the contracted semigroup algebra A of a finite inverse semigroup S over an arbitrary field there is given a basis, whose elements together with the zero of the algebra A form a semigroup ¯S, which is the 0-direct union of Brandt semigroups, whose description is given in terms of the semigroup S. With the help of this basis there is found the number of nonzero irreducible modular representations of the semigroup S by matrices over an algebraically closed field of nonzero characteristic.
8 citations
8 citations
TL;DR: In this article, the authors define the radical ϱ ≥ ≥ 0 (k ≥ 0) of a relation ϱ on an arbitrary semigroup and define various types of k-regularity of semigroups.
Abstract: In this paper we define the radical ϱ
k
(k∈Z
+) of a relation ϱ on an arbitrary semigroup. Also, we define various types of k-regularity of semigroups and various types of k-Archimedness of semigroups. Using these notions we describe the structure of semigroups in which ρ
k
is a band (semilattice) congruence for some Green’s relation.
8 citations
Journal Article•
8 citations