{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:15:44Z","timestamp":1758474944552},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1142\/s021819671950070x","type":"journal-article","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T08:08:17Z","timestamp":1568016497000},"page":"181-216","source":"Crossref","is-referenced-by-count":5,"title":["Cross-connection structure of concordant semigroups"],"prefix":"10.1142","volume":"30","author":[{"given":"P. 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