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On closedness of some permutative posemigroup identities | ||
| Journal of Algebra and Related Topics | ||
| دوره 12، شماره 1، مهر 2024، صفحه 1-12 اصل مقاله (307.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.23645.1498 | ||
| نویسندگان | ||
| R. Alam؛ W. Ashraf* ؛ N. Mohammad Khan | ||
| Department of Mathematics, Aligarh Muslim University, Aligarh, India | ||
| چکیده | ||
| As we know that all non-trivial permutation identities are not preserved under epimorphisms of partially ordered semigroups. In this paper towards this open problem, first we show that certain non-trivial identities in conjunction with the permutation identity $z_1z_2 \cdots z_n=z_{i_1}z_{i_2}\cdots z_{i_n}~ (n\geq2)$ with $i_n \neq n ~~[i_1 \neq 1]$ are preserved under epimorphisms of partially ordered semigroups. Further, we extend a result of Ahanger and Shah which showed that the center of a partially ordered semigroup $S$ is closed in $S$ and show that the normalizer of any element of a partially ordered semigroup $S$ is closed in $S$. | ||
| کلیدواژه‌ها | ||
| Posemigroups؛ Dominion؛ Zigzag؛ Variety | ||
| مراجع | ||
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1. S. A. Ahanger, A. H. Shah, Epimorphisms, Dominions and Varieties of Commutative Posemigroups, Asian European Journal of Mathematics (D.O.I: 10.1142/S1793557121500480) (2020). 2. S. A. Ahanger, A. H. Shah, N. M. Khan, Permutative Varieties of Posemigroups, Comm. Algebra, (7) 49 (2021, 2758-2774. 3. L. S. Bloom, Variety of ordered algebras, J. Comput. System Sci. 13 (1976), 200-212. 4. P. M. Higgins, Saturated and Epimorphically Closed Varieties of Semigroups, J. Austral. Math. soc. (Series A) 36 (1984),153-175 . 5. J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford (1995). 6. N. M. Khan, On Saturated Varieties and Consequences of Permutative Identities, J. Austral. Math. soc. (Series A) 38 (1985), 186-197. 7. N. M. Khan, Epimorphically Closed Permutation Varieties, Trans. Amer. Math. Soc. (2) 287 (1985), 507-528. 8. N. Sohail and L. Tart, Dominions, Zizags and epimorphisms for partially ordered semigroup, Acta Et Commentationes Universitatis Tartuensis De Mathematica, (1) 18 (2014), 81-91. | ||
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آمار تعداد مشاهده مقاله: 231 تعداد دریافت فایل اصل مقاله: 439 |
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