Axioms for unary semigroups via division operations

Bibliographic Details
Main Author: Araújo, João
Publication Date: 2012
Other Authors: Kinyon, Michael
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.2/3796
Summary: When a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.
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spelling Axioms for unary semigroups via division operationsBigroupoidClifford semigroupsCompletely regularE-inversive semigroupsInverse semigroupsWhen a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.Repositório AbertoAraújo, JoãoKinyon, Michael2015-03-23T14:31:59Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3796eng0092-78721532-412510.1080/00927872.2010.536604info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-26T09:43:47Zoai:repositorioaberto.uab.pt:10400.2/3796Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T21:06:26.049785Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Axioms for unary semigroups via division operations
title Axioms for unary semigroups via division operations
spellingShingle Axioms for unary semigroups via division operations
Araújo, João
Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
title_short Axioms for unary semigroups via division operations
title_full Axioms for unary semigroups via division operations
title_fullStr Axioms for unary semigroups via division operations
title_full_unstemmed Axioms for unary semigroups via division operations
title_sort Axioms for unary semigroups via division operations
author Araújo, João
author_facet Araújo, João
Kinyon, Michael
author_role author
author2 Kinyon, Michael
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Araújo, João
Kinyon, Michael
dc.subject.por.fl_str_mv Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
topic Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
description When a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01T00:00:00Z
2015-03-23T14:31:59Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/3796
url http://hdl.handle.net/10400.2/3796
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0092-7872
1532-4125
10.1080/00927872.2010.536604
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