On An Application Of The Suslin Monic Polynomial Theorem (I)

Abstract

In this paper our main theorem states the following, Main Theorem : Let B denote the polynomial ring D[x1,.... ,xn] , in the commuting indeterminates x i over a division ring D . Let M be a finitely generated B-module . Let B m denote the polynomial subring of B , namely D[x1,.... ,xm] , in m , indeterminates , where m is an integer such that 0 ? m ? n , with B0 =D, and Bn =B . Then Krull dimension (M) is m , 0 ? m ? n , if and only if M is a non torsion B m module such that for any positive integer k , k > m , M is a torsion B k module . We then also state and announce a generalisation of the above theorem .