Algorithms on parametric decomposition of monomial ideals

研究成果: 雜誌貢獻文章

1 引文 斯高帕斯(Scopus)


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.

頁(從 - 到)3435-3456
期刊Communications in Algebra
出版狀態已發佈 - 2002 七月 1

ASJC Scopus subject areas

  • Algebra and Number Theory

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