On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents
© 2017 Taylor & Francis. Let ΠL 1 denote a direct power of L 1 , 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∈S 1 and the left ample...
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th-cmuir.6653943832-400712017-09-28T03:57:39Z On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents Billhardt B. Chaiya Y. Laysirikul E. Sangkhanan K. Sanwong J. © 2017 Taylor & Francis. Let ΠL 1 denote a direct power of L 1 , 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∈S 1 and the left ample condition e 2 = 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 ΠL 1 -embeddable band by a right cancellative monoid, giving a partial answer to a question raised in [1]. 2017-09-28T03:57:39Z 2017-09-28T03:57:39Z 11 Journal 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/6653943832/40071 |
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© 2017 Taylor & Francis. Let ΠL 1 denote a direct power of L 1 , 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∈S 1 and the left ample condition e 2 = 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 ΠL 1 -embeddable band by a right cancellative monoid, giving a partial answer to a question raised in [1]. |
| format |
Journal |
| author |
Billhardt B. Chaiya Y. Laysirikul E. Sangkhanan K. Sanwong J. |
| spellingShingle |
Billhardt B. Chaiya Y. Laysirikul E. Sangkhanan K. Sanwong J. On left quasi-ample semigroups with ΠL<sup>1</sup>-embeddable band of idempotents |
| author_facet |
Billhardt B. Chaiya Y. Laysirikul E. Sangkhanan K. Sanwong J. |
| author_sort |
Billhardt B. |
| 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 |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85016967196&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40071 |
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1681421742269005824 |