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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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155148 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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