Cross-connections and variants of the full transformation semigroup

Muhammed, P. A. Azeef: Cross-connections and variants of the full transformation semigroup. Acta scientiarum mathematicarum, (84) 3-4. pp. 377-399. (2018)

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Abstract

Cross-connection theory propounded by Nambooripad describes the ideal structure of a regular semigroup using the categories of principal left (right) ideals. A variant T X of the full transformation semigroup (TX, ·) for an arbitrary θ ∈ TX is the semigroup T X = (TX, ∗) with the binary operation α∗ β = α· θ · β where α, β ∈ TX. In this article, we describe the ideal structure of the regular part Reg(T X) of the variant of the full transformation semigroup using cross-connections. We characterize the constituent categories of Reg(T X) and describe how they are cross-connected by a functor induced by the sandwich transformation θ. This leads us to a structure theorem for the semigroup and gives the representation of Reg(T X) as a cross-connection semigroup. Using this, we give a description of the biordered set and the sandwich sets of the semigroup.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2018
Volume: 84
Number: 3-4
Page Range: pp. 377-399
ISSN: 0001-6969
DOI: https://doi.org/10.14232/actasm-017-044-z
Uncontrolled Keywords: Félcsoport, Matematika
Additional Information: Bibliogr.: p. 397-399. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Jan. 30. 05:13
Last Modified: 2019. Sep. 09. 13:44
URI: http://acta.bibl.u-szeged.hu/id/eprint/56920

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