On Invariant Factors of Primary Components of Square Matrices

In this paper we introduce the P-primary component of a square matrix A over any arbitrary commutative eld K, where P is an irreducible polynomial of K[X]. We use some deep results on module theory over a PID to establish the links between the invariant factors of A and the invariant factors of its primary component. We also prove that if A a P-primary matrix. Then B=P(A) is a nilpotent matrix of type = ( 1; ; 1 | {z } degP ; ; r; ; r | {z } degP ). Where = ( 1; ; r) is the