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Title: Cross-connection structure of concordant semigroups
Authors: Azeef Muhammed, P. A.
Romeo, P. G.
Nambooripad, K. S. S.
Issue Date: 2020
Publisher: World Scientific Publishing Co. Pte Ltd
Citation: Azeef Muhammed P. A. Cross-connection structure of concordant semigroups / P. A. Azeef Muhammed, P. G. Romeo, K. S. S. Nambooripad. — DOI 10.1142/S021819671950070X // International Journal of Algebra and Computation. — 2020. — Vol. 30. — Iss. 1. — P. 181-216.
Abstract: Cross-connection theory provides the construction of a semigroup from its ideal structure using small categories. A concordant semigroup is an idempotent-connected abundant semigroup whose idempotents generate a regular subsemigroup. We characterize the categories arising from the generalized Green relations in the concordant semigroup as consistent categories and describe their interrelationship using cross-connections. Conversely, given a pair of cross-connected consistent categories, we build a concordant semigroup. We use this correspondence to prove a category equivalence between the category of concordant semigroups and the category of cross-connected consistent categories. In the process, we illustrate how our construction is a generalization of the cross-connection analysis of regular semigroups. We also identify the inductive cancellative category associated with a pair of cross-connected consistent categories. © 2020 World Scientific Publishing Company.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85073733011
PURE ID: 12248797
ISSN: 2181967
DOI: 10.1142/S021819671950070X
metadata.dc.description.sponsorship: The first author acknowledges the financial support of the Competitiveness Enhancement Program of Ural Federal University, Russia during the preparation of this paper.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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