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Title: Cross-connections and variants of the full transformation semigroup
Authors: Muhammed, P. A. A.
Issue Date: 2018
Publisher: University of Szeged
Citation: Muhammed P. A. A. Cross-connections and variants of the full transformation semigroup / P. A. A. Muhammed. — DOI 10.14232/actasm-017-044-z // Acta Scientiarum Mathematicarum. — 2018. — Vol. 84. — Iss. 3-4. — P. 377-399.
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 TX θ of the full transformation semigroup (TX, ·) for an arbitrary θ ∈ TX is the semigroup TX θ = (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(TX θ ) of the variant of the full transformation semigroup using cross-connections. We characterize the constituent categories of Reg(TX θ ) 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(TX θ ) as a cross-connection semigroup. Using this, we give a description of the biordered set and the sandwich sets of the semigroup. © 2018 University of Szeged. All rights reserved.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85057732354
PURE ID: 8424060
ISSN: 16969
DOI: 10.14232/actasm-017-044-z
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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