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

摘要

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 Gaff_n(R) of Rn is introduced, then Schützenberger groups of [InlineEquation not available: see fulltext.]-classes, principal factors and group [InlineEquation not available: see fulltext.]-classes of the monoid Gaff_n(R) are investigated. As corollaries, basic numerical information of Gaff_n(R) is given.