تقرير
Regular semigroups weakly generated by one element
| العنوان: | Regular semigroups weakly generated by one element |
|---|---|
| المؤلفون: | Oliveira, Luís |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, 20M17 (Primary), 20M05, 20M10 (Secondary) |
| الوصف: | In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup $F_1$ weakly generated by x such that all other regular semigroups weakly generated by x are homomorphic images of $F_1$. We define $F_1$ using a presentation where both sets of generators and relations are infinite. Nevertheless, the word problem for this presentation is decidable. We describe a canonical form for the congruence classes given by this presentation, and explain how to obtain it. We end the paper studying the structure of $F_1$. In particular, we show that the `free regular semigroup $FI_2$ weakly generated by two idempotents "is isomorphic to a regular subsemigroup of $F_1$ weakly generated by {xx',x'x}. Comment: 38 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.08461 |
| رقم الأكسشن: | edsarx.2302.08461 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |