Algorithms on parametric decomposition of monomial ideals

Research output: Contribution to journalArticle

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Abstract

Heinzer, Mirbagheri, Ratliff, and Shah investigate parametric decomposition of monomial ideals on a regular sequence of a commutative ring R with identity 1 and prove that if every finite intersection of monomial ideals in R is again a monomial ideal, then each monomial ideal has a unique irredundant parametric decomposition. Sturmfels, Trung, and Vogels prove a similar result without the uniqueness. Bayer, Peeva, and Strumfels study generic monomial ideals, that is monomial ideals in the polynomial ring such that no variable appears with the same nonzero exponent in two different minimal generators, and for these ideals they prove the uniqueness of the irredundant irreducible decompositions and give an algorithm to construct this unique irredundant irreducible decomposition. In this paper, we present three algorithms for finding the unique irredundant irreducible decomposition of any monomial ideal.

Original languageEnglish
Pages (from-to)3435-3456
Number of pages22
JournalCommunications in Algebra
Volume30
Issue number7
DOIs
Publication statusPublished - 2002 Jul 1

Fingerprint

Monomial Ideals
Decompose
Uniqueness
Regular Sequence
Polynomial ring
Bayes
Commutative Ring
Intersection
Exponent
Generator

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Algorithms on parametric decomposition of monomial ideals. / Liu, Jung Chen.

In: Communications in Algebra, Vol. 30, No. 7, 01.07.2002, p. 3435-3456.

Research output: Contribution to journalArticle

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