An Algorithm to Compute a Primary Decomposition of Modules in Polynomial Rings over the Integers

2014/08/19 by Idrees, Nazeran, Pfister, Gerhard, Sadiq, Afshan
#13E05 #13P99 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.4343

Abstract

We present an algorithm to compute the primary decomposition of a submodule N of the free module \Z[x₁, …, 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[x₁, …, x_n]^m /N) in \Z[x₁,…,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 \sc Singular.

Related

• Primary decomposition of modules: a computational differential approach
• Associated prime submodules of finitely generated modules
• On primary decomposition of modules
• Computation of the Minimal Associated Primes
• Primary Decomposition with Differential Operators