The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929650994774016 |
|---|---|
| author | Gutik, Oleg Shchypel, Maksym |
| author_facet | Gutik, Oleg Shchypel, Maksym |
| contents | We study algebraic properties of the semigroup $\mathscr{O\!\!I\!}_n(L)$ of finite partial order isomorphisms of the rank $\leq n$ of an infinite linearly ordered set $(L,\leqslant)$. In particular we describe its idempotents, the natural partial order and Green's relations on $\mathscr{O\!\!I\!}_n(L)$. It is proved that the semigroup $\mathscr{O\!\!I\!}_n(L)$ is stable and it contains tight ideal series. Moreover, we show that the semigroup $\mathscr{O\!\!I\!}_n(L)$ admits only Rees' congruences and every its homomorphic image is a semigroup with tight ideal series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set Gutik, Oleg Shchypel, Maksym Group Theory 20M15, 20M50, 18B40 We study algebraic properties of the semigroup $\mathscr{O\!\!I\!}_n(L)$ of finite partial order isomorphisms of the rank $\leq n$ of an infinite linearly ordered set $(L,\leqslant)$. In particular we describe its idempotents, the natural partial order and Green's relations on $\mathscr{O\!\!I\!}_n(L)$. It is proved that the semigroup $\mathscr{O\!\!I\!}_n(L)$ is stable and it contains tight ideal series. Moreover, we show that the semigroup $\mathscr{O\!\!I\!}_n(L)$ admits only Rees' congruences and every its homomorphic image is a semigroup with tight ideal series. |
| title | The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set |
| topic | Group Theory 20M15, 20M50, 18B40 |
| url | https://arxiv.org/abs/2411.03268 |