On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band
It is well known that the semigroup \(\mathcal{B}(S)\) of all bi-ideal elements of an \(le\)-semigroup \(S\) is a band if and only if \(S\) is both regular and intra-regular. Here we show that \(\mathcal{B}(S)\) is a band if and only if it is a normal band and give a complete characterization of the...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2016
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/141 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1412016-01-12T07:40:37Z On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band Bhuniya, A. K. Kumbhakar, M. bi-ideal elements, duo; intra-regular, lattice-ordered semigroup, locally testable, normal band, regular 06F05 It is well known that the semigroup \(\mathcal{B}(S)\) of all bi-ideal elements of an \(le\)-semigroup \(S\) is a band if and only if \(S\) is both regular and intra-regular. Here we show that \(\mathcal{B}(S)\) is a band if and only if it is a normal band and give a complete characterization of the \(le\)-semigroups \(S\) for which the associated semigroup \(\mathcal{B}(S)\) is in each of the seven nontrivial subvarieties of normal bands. We also show that the set \(\mathcal{B}_{m}(S)\) of all minimal bi-ideal elements of \(S\) forms a rectangular band and that \(\mathcal{B}_{m}(S)\) is a bi-ideal of the semigroup~\(\mathcal{B(S)}\). Lugansk National Taras Shevchenko University 2016-01-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/141 Algebra and Discrete Mathematics; Vol 20, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/141/37 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
bi-ideal elements duo; intra-regular lattice-ordered semigroup locally testable normal band regular 06F05 |
| spellingShingle |
bi-ideal elements duo; intra-regular lattice-ordered semigroup locally testable normal band regular 06F05 Bhuniya, A. K. Kumbhakar, M. On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| topic_facet |
bi-ideal elements duo; intra-regular lattice-ordered semigroup locally testable normal band regular 06F05 |
| format |
Article |
| author |
Bhuniya, A. K. Kumbhakar, M. |
| author_facet |
Bhuniya, A. K. Kumbhakar, M. |
| author_sort |
Bhuniya, A. K. |
| title |
On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| title_short |
On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| title_full |
On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| title_fullStr |
On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| title_full_unstemmed |
On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| title_sort |
on the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band |
| description |
It is well known that the semigroup \(\mathcal{B}(S)\) of all bi-ideal elements of an \(le\)-semigroup \(S\) is a band if and only if \(S\) is both regular and intra-regular. Here we show that \(\mathcal{B}(S)\) is a band if and only if it is a normal band and give a complete characterization of the \(le\)-semigroups \(S\) for which the associated semigroup \(\mathcal{B}(S)\) is in each of the seven nontrivial subvarieties of normal bands. We also show that the set \(\mathcal{B}_{m}(S)\) of all minimal bi-ideal elements of \(S\) forms a rectangular band and that \(\mathcal{B}_{m}(S)\) is a bi-ideal of the semigroup~\(\mathcal{B(S)}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/141 |
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AT bhuniyaak onthelesemigroupswhosesemigroupofbiidealelementsisanormalband AT kumbhakarm onthelesemigroupswhosesemigroupofbiidealelementsisanormalband |
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2024-04-12T06:27:37Z |
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2024-04-12T06:27:37Z |
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