Isomorphism Theorems for Semigroups of Order-preserving Full Transformations
Phichet Jitjankarn · arXiv (Cornell University) · 2012
For each subchain $\C'$ of a chain $\C$, the semigroup of all full order-preserving transformations, $\a:\C\rightarrow \C'$ satisfying if $x\leq y$ implies $x\a\leq y\a$ for $x,y\in \C$, is denoted by $T_{OP}(\C,\C')$. It is well-known that for any posets $X$ and $Y$, $T_{OP}(X)\cong T_{OP}(Y)$ if and only if $X$ and $Y$ are either order-isomorphic or order-anti-isomorphic. The purpose of this paper is to show the analogous results for $T_{OP}(X,X')$ and $T_{OP}(Y,Y')$.