SEMIGROUPS OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE

Abstract

Abstract In 1975, Symons described the automorphisms of the semigroup T ( X , Y ) consisting of all total transformations from a set X into a fixed subset Y of X . Recently Sanwong, Singha and Sullivan determined all maximal (and all minimal) congruences on T ( X , Y ), and Sommanee studied Green’s relations in T ( X , Y ). Here, we describe Green’s relations and ideals for the semigroup T ( V , W ) consisting of all linear transformations from a vector space V into a fixed subspace W of V .