A Canonical Set For Matrices Over a Principal Ideal Ring Modulo m

Abstract

If m ∈ P where P is a p.i.r. (principal ideal ring), then P/ {m} is a commutative ring with unit element. The elements of this ring are designated by ā where a ∈ P. The set of square matrices of order n with elements in P/ {m} forms a ring with unit element. The units in this ring are the unimodular matrices, i.e., the matrices whose determinants are units of P/ {m}.