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Finite coverings of semigroups and related structures | ||
| International Journal of Group Theory | ||
| مقاله 30، دوره 12، شماره 3، آذر 2023، صفحه 205-222 اصل مقاله (440.07 K) | ||
| نوع مقاله: Ischia Group Theory 2020/2021 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.131538.1759 | ||
| نویسندگان | ||
| Casey R. Donoven* 1؛ Luise-Charlotte Kappe2 | ||
| 1Department of Mathematics, Montana State University, Havre, MT, 59501, USA | ||
| 2Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA | ||
| چکیده | ||
| For a semigroup $S$, the covering number of $S$ with respect to semigroups, $\sigma_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$. This article investigates covering numbers of semigroups and analogously defined covering numbers of inverse semigroups and monoids. Our three main theorems give a complete description of the covering number of finite semigroups, finite inverse semigroups, and monoids (modulo groups and infinite semigroups). For a finite semigroup that is neither monogenic nor a group, its covering number is two. For all $n\geq 2$, there exists an inverse semigroup with covering number $n$, similar to the case of loops. Finally, a monoid that is neither a group nor a semigroup with an identity adjoined has covering number two as well. | ||
| کلیدواژه‌ها | ||
| Semigroup؛ covering number؛ inverse semigroup؛ monoid | ||
| مراجع | ||
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