Generalized affine transformation monoid of a free module of finite rank over finite chain rings

Abstract

Let R be a finite commutative chain ring, n a positive integer and Rn the free R-module of rank n consisting of column vectors over R. The generalized affine transformation monoid Gaffn(R) of Rn is introduced, then Schutzenberger groups of Open image in new window-classes, principal factors and group Open image in new window-classes of the monoid Gaffn(R) are investigated. As corollaries, basic numerical information of Gaffn(R) is given.