ON THE MULTIPLICATIVE MONOID OF n x n MATRICES OVER ARTINIAN CHAIN RINGS

Let R be an Artinian chain ring with a principal maximal ideal. We investigate properties of matrices over R and give matrix representations of R-submodules of R(n) first, then consider Green's relations, Green's relation equivalent classes, Schutzenberger groups of D-classes, principal factors, and group H-classes of the multiplicative monoid M(n) (R) of n x n matrices over R. Furthermore, we show that M(n) (R) is an eventually regular semigroup and derive basic numerical information of M(n) (R) when R is finite.