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.
Adams, W. W. and Loustaunau, P., An Introduction to Gröbner bases, Graduate studies in mathematics, vol. 3, American Mathematical Scociety, 2003.
Loustaunau P., '', in Graduate studies in mathematics, (2003) -.
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Ayoub, C. W., The Decomposition Theorem for Ideals in Polynomial Rings over a Domain, Journal of Algebra, 76 (1982), 99–110.
Ayoub C. W., 'The Decomposition Theorem for Ideals in Polynomial Rings over a Domain' (1982) 76Journal of Algebra: 99-110.
Ayoub C. W.The Decomposition Theorem for Ideals in Polynomial Rings over a DomainJournal of Algebra19827699110)| false