Regularity and Green's Relations for Generalized Semigroups of Transformations with Invariant Set

Lei Sun


Let ${\cal T}_X$ be the full transformation semigroup on a set $X$.
For $Y\subseteq X$, the semigroup $S(X,Y) =\{ f\in {\cal T}_X: f(Y)\subseteq Y\}$ is a subsemigroup of ${\cal T}_ X $. Fix an element $\theta\in S(X,Y)$ and for $f,g\in S(X,Y)$, define a new operation $*$ on $S(X,Y)$ by $f* g=f\theta g$ where $f\theta g$ denotes the produce of $g,\theta$ and $f$ in the original sense. Under this operation, the semigroup $S(X,Y)$ forms a semigroup which is called generalized semigroup of $S(X,Y)$ with the sandwich function $\theta$ and denoted by $S(X,Y,*_\theta)$. In this paper we first characterize the regular elements and then describe Green's relations for the semigroup $S(X,Y,*_\theta)$.

Full Text:



License URL:

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the '' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.