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Title: Inductive groupoids and cross-connections of regular semigroups
Authors: Muhammed, P. A. A.
Volkov, M. V.
Issue Date: 2019
Publisher: Springer Netherlands
Citation: Muhammed P. A. A. Inductive groupoids and cross-connections of regular semigroups / P. A. A. Muhammed, M. V. Volkov. — DOI 10.1007/s10474-018-0888-6 // Acta Mathematica Hungarica. — 2019. — Vol. 157. — Iss. 1. — P. 80-120.
Abstract: There are two major structure theorems for an arbitrary regular semigroup using categories, both due to Nambooripad. The first construction using inductive groupoids departs from the biordered set structure of a given regular semigroup. This approach belongs to the realm of the celebrated Ehresmann–Schein–Nambooripad Theorem and its subsequent generalisations. The second construction is a generalisation of Grillet’s work on cross-connected partially ordered sets, arising from the principal ideals of the given semigroup. In this article, we establish a direct equivalence between these two seemingly different constructions. We show how the cross-connection representation of a regular semigroup may be constructed directly from the inductive groupoid of the semigroup, and vice versa. © 2018, Akadémiai Kiadó, Budapest, Hungary.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85058111064
PURE ID: 9071508
ISSN: 2365294
DOI: 10.1007/s10474-018-0888-6
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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