On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents

© 2017 Taylor & Francis. Let ΠL1denote a direct power of L1, the two-element left zero semigroup with identity adjoined. A semigroup S is called left quasi-ample if for each a∈S there exists a unique idempotent a+∈S such that xa = ya ⇔ xa+= ya+for all x, y∈S1and the left ample condition e2= e...

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Main Authors: Bernd Billhardt, Yanisa Chaiya, Ekkachai Laysirikul, Kritsada Sangkhanan, Jintana Sanwong
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Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/57509
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-575092018-09-05T03:44:10Z On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents Bernd Billhardt Yanisa Chaiya Ekkachai Laysirikul Kritsada Sangkhanan Jintana Sanwong Mathematics © 2017 Taylor & Francis. Let ΠL1denote a direct power of L1, the two-element left zero semigroup with identity adjoined. A semigroup S is called left quasi-ample if for each a∈S there exists a unique idempotent a+∈S such that xa = ya ⇔ xa+= ya+for all x, y∈S1and the left ample condition e2= e ⇒ (ae)+a = ae holds. Generalizing a recent result in [3], we prove that the semigroups in the title are embeddable into certain transformation semigroups. Our embedding provides an easy way to construct (finite) proper covers for (finite) such semigroups. Moreover, we show that each proper such semigroup is embeddable into a semidirect product of a ΠL1-embeddable band by a right cancellative monoid, giving a partial answer to a question raised in [1]. 2018-09-05T03:44:10Z 2018-09-05T03:44:10Z 2017-11-02 Journal 15324125 00927872 2-s2.0-85016967196 10.1080/00927872.2017.1291811 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85016967196&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57509
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Bernd Billhardt
Yanisa Chaiya
Ekkachai Laysirikul
Kritsada Sangkhanan
Jintana Sanwong
On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
description © 2017 Taylor & Francis. Let ΠL1denote a direct power of L1, the two-element left zero semigroup with identity adjoined. A semigroup S is called left quasi-ample if for each a∈S there exists a unique idempotent a+∈S such that xa = ya ⇔ xa+= ya+for all x, y∈S1and the left ample condition e2= e ⇒ (ae)+a = ae holds. Generalizing a recent result in [3], we prove that the semigroups in the title are embeddable into certain transformation semigroups. Our embedding provides an easy way to construct (finite) proper covers for (finite) such semigroups. Moreover, we show that each proper such semigroup is embeddable into a semidirect product of a ΠL1-embeddable band by a right cancellative monoid, giving a partial answer to a question raised in [1].
format Journal
author Bernd Billhardt
Yanisa Chaiya
Ekkachai Laysirikul
Kritsada Sangkhanan
Jintana Sanwong
author_facet Bernd Billhardt
Yanisa Chaiya
Ekkachai Laysirikul
Kritsada Sangkhanan
Jintana Sanwong
author_sort Bernd Billhardt
title On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
title_short On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
title_full On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
title_fullStr On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
title_full_unstemmed On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
title_sort on left quasi-ample semigroups with πl<sup>1</sup>-embeddable band of idempotents
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85016967196&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/57509
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