Cross-Connections in Clifford Semigroups

P. A. Azeef Muhammed; C. S. Preenu

doi:10.1007/978-981-99-6349-2_1

Cross-Connections in Clifford Semigroups

P. A. Azeef Muhammed, C. S. Preenu

School of Computer, Data and Mathematical Sciences

University of Kerala

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

Abstract

An inverse Clifford semigroup (often referred to as just a Clifford semi-group) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups (Clifford in Ann Math 42(4):1037-1049 (1941), [6]). In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup. S, we show that the semigroup.T L(S) of normal cones is isomorphic to the original semigroup. S, even when. S is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.

Original language	English
Title of host publication	Semigroups, Algebras and Operator Theory - ICSAOT 2022
Editors	A.A. Ambily, V.B. Kiran Kumar
Publisher	Springer
Pages	3-9
Number of pages	7
ISBN (Print)	9789819963485
DOIs	https://doi.org/10.1007/978-981-99-6349-2_1
Publication status	Published - 2023
Event	International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022 - Cochin, India Duration: 28 Mar 2022 → 31 Mar 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	436
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022
Country/Territory	India
City	Cochin
Period	28/03/22 → 31/03/22

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.

Keywords

Clifford semigroups
Cross-connections
Inverse semigroups
Normal categories
Semilattices

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10.1007/978-981-99-6349-2_1

Cite this

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title = "Cross-Connections in Clifford Semigroups",

abstract = "An inverse Clifford semigroup (often referred to as just a Clifford semi-group) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups (Clifford in Ann Math 42(4):1037-1049 (1941), [6]). In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup. S, we show that the semigroup.T L(S) of normal cones is isomorphic to the original semigroup. S, even when. S is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.",

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author = "{Azeef Muhammed}, {P. A.} and Preenu, {C. S.}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.; International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022 ; Conference date: 28-03-2022 Through 31-03-2022",

year = "2023",

doi = "10.1007/978-981-99-6349-2_1",

language = "English",

isbn = "9789819963485",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "3--9",

editor = "A.A. Ambily and {Kiran Kumar}, V.B.",

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Azeef Muhammed, PA & Preenu, CS 2023, Cross-Connections in Clifford Semigroups. in AA Ambily & VB Kiran Kumar (eds), Semigroups, Algebras and Operator Theory - ICSAOT 2022. Springer Proceedings in Mathematics and Statistics, vol. 436, Springer, pp. 3-9, International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022, Cochin, India, 28/03/22. https://doi.org/10.1007/978-981-99-6349-2_1

TY - GEN

T1 - Cross-Connections in Clifford Semigroups

AU - Azeef Muhammed, P. A.

AU - Preenu, C. S.

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.

PY - 2023

Y1 - 2023

N2 - An inverse Clifford semigroup (often referred to as just a Clifford semi-group) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups (Clifford in Ann Math 42(4):1037-1049 (1941), [6]). In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup. S, we show that the semigroup.T L(S) of normal cones is isomorphic to the original semigroup. S, even when. S is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.

AB - An inverse Clifford semigroup (often referred to as just a Clifford semi-group) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied classes of semigroups (Clifford in Ann Math 42(4):1037-1049 (1941), [6]). In this short note, we discuss various structural aspects of a Clifford semigroup from a cross-connection perspective. In particular, given a Clifford semigroup. S, we show that the semigroup.T L(S) of normal cones is isomorphic to the original semigroup. S, even when. S is not a monoid. Hence, we see that cross-connection description degenerates in Clifford semigroups. Further, we specialise the discussion to provide the description of the cross-connection structure in an arbitrary semilattice, also.

KW - Clifford semigroups

KW - Cross-connections

KW - Inverse semigroups

KW - Normal categories

KW - Semilattices

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T3 - Springer Proceedings in Mathematics and Statistics

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BT - Semigroups, Algebras and Operator Theory - ICSAOT 2022

A2 - Ambily, A.A.

A2 - Kiran Kumar, V.B.

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Y2 - 28 March 2022 through 31 March 2022

ER -

Cross-Connections in Clifford Semigroups

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