An algorithm to compute a primary decomposition of modules in polynomial rings over the integers

Nazeran Idrees; Gerhard Pfister; Afshan Sadiq

doi:10.1556/sscmath.52.2015.1.1296

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 1

An algorithm to compute a primary decomposition of modules in polynomial rings over the integers

Authors:

Nazeran Idrees

Nazeran Idrees GC University Department of Mathematics Kotwali Road, Jinnah Town Faisalabad, Punjab 38000 Faisalabad Pakistan

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Gerhard Pfister

Gerhard Pfister University of Kaiserslautern Department of Mathematics Erwin-Schrödinger-Str. 67663 Kaiserslautern Germany

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Afshan Sadiq

Afshan Sadiq Jazan University Department of Mathematics P.O. Box 114 Jazan Saudia Arabia

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Pages:: 40–51

Online Publication Date:: 17 Mar 2015

Publication Date:: 01 Mar 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.52.2015.1.1296

Keywords:: Primary 13P99; 13E05; Gröbner bases; primary decomposition; primary modules; associated primes; pseudo primary; localization; extraction

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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 Singular.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Gábor SÁGI (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language	English French German
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ISSN	0081-6906 (Print)
ISSN	1588-2896 (Online)