Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101899
Title: Cross-connections of linear transformation semigroups
Authors: Muhammed, P. A. A.
Issue Date: 2018
Publisher: Springer New York LLC
Citation: Muhammed P. A. A. Cross-connections of linear transformation semigroups / P. A. A. Muhammed. — DOI 10.1007/s00233-018-9942-5 // Semigroup Forum. — 2018. — Vol. 97. — Iss. 3. — P. 457-470.
Abstract: Cross-connection theory developed by Nambooripad is the construction of a regular semigroup from its principal left (right) ideals using categories. We use the cross-connection theory to study the structure of the semigroup Sing(V) of singular linear transformations on an arbitrary vector space V over a field K. There is an inbuilt notion of duality in the cross-connection theory, and we observe that it coincides with the conventional algebraic duality of vector spaces. We describe various cross-connections between these categories and show that although there are many cross-connections, upto isomorphism, we have only one semigroup arising from these categories. But if we restrict the categories suitably, we can construct some interesting subsemigroups of the variants of the linear transformation semigroup. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: CROSS-CONNECTIONS
DUAL
LINEAR TRANSFORMATION SEMIGROUP
NORMAL CATEGORY
REGULAR SEMIGROUP
VARIANT
URI: http://hdl.handle.net/10995/101899
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85057724512
PURE ID: 8431980
ISSN: 371912
DOI: 10.1007/s00233-018-9942-5
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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