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On (m, k) -type elements in the ring of integers modulo n |
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| รหัสดีโอไอ | |
| Creator | 1. Phoschanun Ratanaburee 2. Montakarn Petapirak 3. Sompong Chuysurichay |
| Title | On (m, k) -type elements in the ring of integers modulo n |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2022 |
| Journal Title | Songklanakarin Journal of Science an Technology (SJST) |
| Journal Vol. | 44 |
| Journal No. | 5 |
| Page no. | 1179-1184 |
| Keyword | (m, k)-type elements, ring of integers modulo n, m-potents, cyclic semigroup, cyclic group |
| URL Website | https://sjst.psu.ac.th/ |
| ISSN | 0125-3395 |
| Abstract | An element a in a ring R is said to be of (m, k)-type if am = ak where m and k are positive integers with m > k ? 1. LetXn(m, k) be the set of all (m, k)-type elements, X*n(m, k) be the set of all nonzero (m, k)-type elements, and Sn(m, k) be the set ofall nonunit (m, k)-type elements in the ring of integers modulo n. In this paper, we study the algebraic structures of Xn(m, k),X*n(m, k) and Sn(m, k) and characterize all values of n, m, and k for which Xn(m, k) and Sn(m, k) are cyclic semigroups and X*n(m,k) is a cyclic group. |
