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On (m, n)-ideals and (m, n)-regular ordered semigroups |
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| รหัสดีโอไอ | |
| Creator | 1. Limpapat Bussaban 2. Thawhat Changphas |
| Title | On (m, n)-ideals and (m, n)-regular ordered semigroups |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2559 |
| Journal Title | Songklanakarin Journal of Science and Technology (SJST) |
| Journal Vol. | 38 |
| Journal No. | 2 |
| Page no. | 199-206 |
| Keyword | semigroup,ordered semigroup,(m, n)-ideal,(m, n)-quasi-ideal,(m, n)-regular |
| ISSN | 0125-3395 |
| Abstract | Let m, n be non-negative integers. A subsemigroup A of an ordered semigroup (S, ? , ? is called an (m, n)-ideal of S if(i) AmSAn ? A, and (ii) if x ? A, y ? S such that y ? x, then y ? A. In this paper, necessary and sufficient conditions for every(m, n)-ideal (resp. (m, n)-quasi-ideal) of an (m, n)-ideal (resp. (m, n)-quasi-ideal) A of S is an (m, n)-ideal (resp. (m, n)-quasiideal)of S will be given. Moreover, (m, n)-regularity of S will be discussed. The results obtained extend the results on semigroups(without order) studied by Bogdanovic? (1979). |
