Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102136
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dc.contributor.authorAzeef Muhammed, P. A.en
dc.contributor.authorRajan, A. R.en
dc.date.accessioned2021-08-31T15:02:01Z-
dc.date.available2021-08-31T15:02:01Z-
dc.date.issued2018-
dc.identifier.citationAzeef Muhammed P. A. Cross-connections of the singular transformation semigroup / P. A. Azeef Muhammed, A. R. Rajan. — DOI 10.1142/S0219498818500470 // Journal of Algebra and its Applications. — 2018. — Vol. 17. — Iss. 3. — 1850047.en
dc.identifier.issn2194988-
dc.identifier.otherFinal2
dc.identifier.otherAll Open Access, Green3
dc.identifier.otherhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017515553&doi=10.1142%2fS0219498818500470&partnerID=40&md5=1c0e9dff488fe4dfdf3b5588b5ca8e05
dc.identifier.otherhttp://arxiv.org/pdf/1603.02796m
dc.identifier.urihttp://hdl.handle.net/10995/102136-
dc.description.abstractCross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the cross-connections in the semigroup Sing(X) of all non-invertible transformations on a set X. The categories involved are characterized as the powerset category (X) and the category of partitions π(X). We describe these categories and show how a permutation on X gives rise to a cross-connection. Further, we prove that every cross-connection between them is induced by a permutation and construct the regular semigroups that arise from the cross-connections. We show that each of the cross-connection semigroups arising this way is isomorphic to Sing(X). We also describe the right reductive subsemigroups of Sing(X) with the category of principal left ideals isomorphic to (X). This study sheds light into the more general theory of cross-connections and also provides an alternate way of studying the structure of Sing(X). © 2018 World Scientific Publishing Company.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherWorld Scientific Publishing Co. Pte Ltden
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceJ. Algebra Appl.2
dc.sourceJournal of Algebra and its Applicationsen
dc.subjectCROSS-CONNECTIONSen
dc.subjectNORMAL CATEGORYen
dc.subjectPARTITIONSen
dc.subjectPOWERSETen
dc.subjectREGULAR SEMIGROUPen
dc.subjectTRANSFORMATION SEMIGROUPen
dc.titleCross-connections of the singular transformation semigroupen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.doi10.1142/S0219498818500470-
dc.identifier.scopus85017515553-
local.contributor.employeeAzeef Muhammed, P.A., School of Mathematics, Indian Institute of Science Education and Research, Kerala, Thiruvananthapuram, 695016, India, Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, 620000, Russian Federation
local.contributor.employeeRajan, A.R., Department of Mathematics, University of Kerala, Kerala, Thiruvananthapuram, 695581, India
local.issue3-
local.volume17-
local.contributor.departmentSchool of Mathematics, Indian Institute of Science Education and Research, Kerala, Thiruvananthapuram, 695016, India
local.contributor.departmentDepartment of Mathematics, University of Kerala, Kerala, Thiruvananthapuram, 695581, India
local.contributor.departmentInstitute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, 620000, Russian Federation
local.identifier.pure6509328-
local.identifier.pure15882865-4923-4eb3-82a1-989cca18d751uuid
local.description.order1850047-
local.identifier.eid2-s2.0-85017515553-
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