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  • 1 GC University Department of Mathematics Kotwali Road, Jinnah Town Faisalabad, Punjab 38000 Faisalabad Pakistan
  • 2 University of Kaiserslautern Department of Mathematics Erwin-Schrödinger-Str. 67663 Kaiserslautern Germany
  • 3 Jazan University Department of Mathematics P.O. Box 114 Jazan Saudia Arabia
Open access

We present an algorithm to compute the primary decomposition of a submodule N of the free module ℤ[x1,...,xn]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[x1,...,xn]m/N) in ℤ[x1,...,xn] and then compute the primary components using pseudo-primary decomposition and extraction, following the ideas of Shimoyama-Yokoyama. The algorithms are implemented in Singular.

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