关于链的保向变换
On orientation-preserving transformations of a chain
摘要：
在本文中，我们介绍了一个任意链上的方向保持变换的概念，作为一个自然扩张无限链的著名的概念有限链在1998年推出的McAlister \cite{McAlister:1998}，并独立于1999年由Catarino和希金斯\cite{Catarino&Higgins:1999}。我们考虑有限或无限链$X$上所有保向部分变换的幺半群$\mathscr{POP}(X)$及其子幺半群$\mathscr{OP}(X)$和$\mathscr{POPJ}(X)$，分别是$X$上所有保向完全变换和所有保向部分置换的子幺半群.本文还研究了$X$上所有保序部分变换的幺半群$\mathscr{PO}(X)$及其内射对应物$\mathscr{POJ}(X)$。研究了幺半群$\mathscr{POP}(X)$，$\mathscr{PO}(X)$，$\mathscr{OP}(X)$，$\mathscr{POPJ}(X)$和$\mathscr{POJ}(X)$的正则性，并给出了它们的格林关系的刻画.
英文摘要：
In this paper we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister \cite{McAlister:1998} and, independently, in 1999 by Catarino and Higgins \cite{Catarino&Higgins:1999}. We consider the monoid $\mathscr{POP}(X)$ of all orientation-preserving partial transformations on a finite or infinite chain $X$ and its submonoids $\mathscr{OP}(X)$ and $\mathscr{POPJ}(X)$ of all orientation-preserving full transformations and of all orientation-preserving partial permutations on $X$, respectively. The monoid $\mathscr{PO}(X)$ of all order-preserving partial transformations on $X$ and its injective counterpart $\mathscr{POJ}(X)$ are also considered. We study the regularity and give descriptions of the Green's relations of the monoids $\mathscr{POP}(X)$, $\mathscr{PO}(X)$, $\mathscr{OP}(X)$, $\mathscr{POPJ}(X)$ and $\mathscr{POJ}(X)$.
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