English

An algorithm for primary decomposition in polynomial rings over the integers

Commutative Algebra 2011-08-10 v3

Abstract

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama-Yokoyama resp. Eisenbud-Hunecke-Vasconcelos to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in SINGULAR. Examples and timings are given at the end of the article.

Keywords

Cite

@article{arxiv.1008.2074,
  title  = {An algorithm for primary decomposition in polynomial rings over the integers},
  author = {Gerhard Pfister and Afshan Sadiq and Stefan Steidel},
  journal= {arXiv preprint arXiv:1008.2074},
  year   = {2011}
}

Comments

8 pages

R2 v1 2026-06-21T15:59:53.126Z