AN ALGORITHM TO COMPUTE A PRIMARY DECOMPOSITION OF MODULES IN POLYNOMIAL RINGS OVER THE INTEGERS

We present an algorithm to compute the primary decomposition of a submodule N of the free module Z[x(1),...,x(n)](m). For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N, i.e. the minimal associated primes of the ideal Ann (Z[ x(1),..., x(n)](m) / N) in Z [ x(1),...,x(n)] and then compute the primary components using pseudo-primary decomposition and extraction, following the ideas of Shimoyama-Yokoyama.The algorithms are implemented in SINGULAR.