Green's relations on semigroups of regressive transformations with restricted range

Abstract

© 2016 Academic Publications, Ltd. Let X' be a subposet of a poset X. Define PRE(X, X') be the semigroup under composition of all regressive transformations from a subset of X into X'. Moreover, TRE(X,X')={α ∈PRE(X,X'):dom α=X}. In 2012, C. Namnak and E. Laysirikul [3] investigated the Green's relations on TRE(X) = TRE(X, X). Now, we aim to extend the result of them by study the Green's relations on the semigroups TRE(X, X') and PRE(X, X').