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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TL;DR: In this article, certain subsets of a semigroup S, defined mainly by conditions involving regularity preservation, are considered, and the relationships between the subsets are discussed, and some characterisations of completely simple semigroups are obtained.
Abstract: We consider certain subsets of a semigroup S , defined mainly by conditions involving regularity preservation. In particular, the regular base B( S ) of S may be regarded as a generalisation of the zero ideal in a semigroup with zero; if it non-empty then S is E -inversive. The other subsets considered are related in a natural way either to B( S ) or to the set RP( S ) of regularity-preserving elements in S . In a regular semigroup (equipped with the Hartwig-Nambooripad order) each of these subsets contains either minimal elements only or maximal elements only. The relationships between the subsets are discussed, and some characterisations of completely simple semigroups are obtained.
2 citations
TL;DR: In this paper, a Galois correspondence between the subsemigroups of TX and a particular class of digraphs on X is established. But the correspondence is restricted to the case where the digraph is a proper subsemigroup of S * 9 (S).
Abstract: Let Tx be the full transformation semigroup on the set X and let S be a subsemigroup of TX. We may associate with S a digraph g (S) with X as set of vertices as follows: I -k j E g(S) iff there exists at E S such that a(i) = j. Conversely, for a digraph G having certain properties we may assign a semigroup structure, S(G), to the underlying set of G. We are thus able to establish a "Galois correspondence" between the subsemigroups of TX and a particular class of digraphs on X. In general, S is a proper subsemigroup of S * 9 (S).
2 citations
01 Jan 2010
TL;DR: A regular semigroup S is V-regular if V (ab) ⊆ V (b)V (a) for all a,b ∈ S as discussed by the authors.
Abstract: A regular semigroup S is V-regular if V (ab) ⊆ V (b)V (a) for all a,b ∈ S. A characterization of a V-regular semigroup is given. Congruences on V-regular semigroups are described in terms of certain congruence pairs.
2 citations
TL;DR: The endomorphism semigroup for a class of commutative semigroups, called special semigroup, was studied in this article, where their structures were determined in some important cases.
Abstract: The endomorphism semigroup for a class of commutative semigroups, called special semigroups, will be studied their structures will be determined in some important cases. AMS Classification : 20 Keywords: Special semigroups, freeness, divisibility, direct sums, endomorphism, endomorphism semigroup. doi: 10.3329/jbas.v32i1.2442 Journal of Bangladesh Academy of Sciences , Vol. 32, No. 1, 55-60, 2008
2 citations
TL;DR: In this article, a PO-sextet is defined and a structure of E-unitary regular semigroups is described, which is called PO-SEXTE.
Abstract: In this paper we define a concept of a PO-sextet and describe a structure of E-unitary regular semigroups.
2 citations