On the le-semigroups whose semigroup of bi-ideal elements is a normal band
It is well known that the semigroup 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 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 associate...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155148 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the le-semigroups whose semigroup of bi-ideal elements is a normal band / A.K. Bhuniya, M. Kumbhakar // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 171-181. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749634676391936 |
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| author | Bhuniya, A.K. Kumbhakar, M. |
| author_facet | Bhuniya, A.K. Kumbhakar, M. |
| citation_txt | On the le-semigroups whose semigroup of bi-ideal elements is a normal band / A.K. Bhuniya, M. Kumbhakar // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 171-181. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | It is well known that the semigroup 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 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 B(S) is in each of the seven nontrivial subvarieties of normal bands. We also show that the set Bm(S) of all minimal bi-ideal elements of S forms a rectangular band and that Bm(S) is a bi-ideal of the semigroup B(S).
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| first_indexed | 2025-12-07T21:01:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155148 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T21:01:07Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bhuniya, A.K. Kumbhakar, M. 2019-06-16T09:52:30Z 2019-06-16T09:52:30Z 2015 On the le-semigroups whose semigroup of bi-ideal elements is a normal band / A.K. Bhuniya, M. Kumbhakar // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 171-181. — Бібліогр.: 24 назв. — англ. 1726-3255 2010 MSC:06F05. https://nasplib.isofts.kiev.ua/handle/123456789/155148 It is well known that the semigroup 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 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 B(S) is in each of the seven nontrivial subvarieties of normal bands. We also show that the set Bm(S) of all minimal bi-ideal elements of S forms a rectangular band and that Bm(S) is a bi-ideal of the semigroup B(S). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the le-semigroups whose semigroup of bi-ideal elements is a normal band Article published earlier |
| spellingShingle | On the le-semigroups whose semigroup of bi-ideal elements is a normal band Bhuniya, A.K. Kumbhakar, M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155148 |
| work_keys_str_mv | AT bhuniyaak onthelesemigroupswhosesemigroupofbiidealelementsisanormalband AT kumbhakarm onthelesemigroupswhosesemigroupofbiidealelementsisanormalband |