LINEAR SYSTEMS OF DIOPHANTINE EQUATIONS

Given free modules M subset of L of finite rank f >= 1 over a principal ideal domain R, we give a procedure to construct a basis of L from a basis of M assuming the invariant factors or elementary divisors of L/M are known. Given a matrix A is an element of M-m,M-n(R) of rank r, its nullspace L in R-n is a free R-module of rank f = n - r. We construct a free submodule M of L of rank f naturally associated with A and whose basis is easily computable, we determine the invariant factors of the quotient module L/M and then indicate how to apply the previous procedure to build a basis of L from one of M.