تقرير
The regular part of transformation semigroups that preserve double direction equivalence relation
| العنوان: | The regular part of transformation semigroups that preserve double direction equivalence relation |
|---|---|
| المؤلفون: | Sangkhanan, Kritsada |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, 20M17, 20M19, 20M20 |
| الوصف: | Let $T(X)$ be the full transformation semigroup on a set $X$ under the composition of functions. For any equivalence relation $E$ on $X$, define a subsemigroup $T_{E^*}(X)$ of $T(X)$ by $$T_{E^*}(X)=\{\alpha\in T(X):\text{for all}\ x,y\in X, (x,y)\in E\Leftrightarrow (x\alpha,y\alpha)\in E\}.$$ In this paper, we show that the regular part of $T_{E^*}(X)$, denoted $\mathrm{Reg}(T)$, is the largest regular subsemigroup of $T_{E^*}(X)$. Then its Green's relations and ideals are described. Moreover, we find the kernel of $\mathrm{Reg}(T)$ which is a right group and can be written as a union of symmetric groups. Finally, we prove that every right group can be embedded in that kernel. Comment: 12 pages, part of this work was presented in the Workshop on General Algebra / Arbeitstagung Allgemeine Algebra (AAA102), University of Szeged, Hungary, June 24-26, 2022 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.08932 |
| رقم الأكسشن: | edsarx.2306.08932 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |