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|Title:||Cross-connection structure of concordant semigroups|
|Authors:||Azeef Muhammed, P. A.|
Romeo, P. G.
Nambooripad, K. S. S.
|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.|
INDUCTIVE CANCELLATIVE CATEGORY
|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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