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REGULAR RIGHT SUBDIRECTLY IRREDUCIBLE SEMIGROUPS | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 فروردین 1402 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.71031.2363 | ||
| نویسندگان | ||
Samira Hosseinzadeh Alikhalaji1؛ Mojtaba Sedaghatjoo  2
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| 1Science and Research Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran | ||
| چکیده | ||
| The main objective of this paper is characterizing regular right subdirectly irreducible semigroups. Our approach to deal with this issue is considering a semigroup $S$ as a right $S$-act over itself and unifying our previous results on the notion of right uniform semigroups to reach the main target of this work. As a result, regular commutative subdirectly irreducible semigroups are characterized. Meanwhile, we investigate conditions under which semigroups $S$ and $S^1$($S$ and $S^0$) are simultaneously right subdirectly irreducible or right irreducible or right uniform. Considering Birkhoff’s theorem, stating that any algebra A is isomorphic to a subdirect product of subdirectly irreducible algebras (which are homomorphic images of A), equivalently, any variety is determined by its subdirectly irreducible members [1, Theorem 9.6], structure of subdirectly irreducible semigroups (semi- groups with least nondiagonal congruences) was a matter of interest in semigroup theory. The first investigation on such semigroups was pioneered by the efforts of Thierrin [15] and Schein [14]. Accordingly, investigating semigroups possessing least nondiagonal right congruences, termed right subdirectly irreducible semigroups, was initiated by Rankin et al. [12], who presented a general account on such semigroups. This class of semigroups is indeed a subclass of subdirectly irreducible semigroups. Regarding that regular semigroups play an undeniable role in semigroup theory, in this paper we characterize regular right subdirectly irreducible semigroups. | ||
| کلیدواژهها | ||
| principal right congruence؛ regular right subdirectly irreducible semigroup؛ uniform act | ||
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آمار تعداد مشاهده مقاله: 59 |
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