The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set

Abstract

We study algebraic properties of the semigroup ${\mathcal{O}\mathcal{I}}_n(L)$ of finite partial order isomorphisms of the rank $\le n$ of an infinite linearly ordered set $(L,⩽)$. In particular we describe its idempotents, the natural partial order and Green's relations on ${\mathcal{O}\mathcal{I}}_n(L)$. It is proved that the semigroup ${\mathcal{O}\mathcal{I}}_n(L)$ is stable and it contains tight ideal series. Moreover, we show that the semigroup ${\mathcal{O}\mathcal{I}}_n(L)$ admits only Rees' congruences and every its homomorphic image is a semigroup with tight ideal series.

7 pages (in Ukrainian)

References in corpus (2)

• Semigroup Closures of Finite Rank Symmetric Inverse Semigroups
• On the semigroup ${\mathbf{B}}_{\omega }^{{\mathcal{F}}_n}$ which is generated by the family ${\mathcal{F}}_n$ of finite bounded intervals of $\omega$

Cited by in corpus (1)

• On compact topologies on the semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set