On ideals with the Rees property

Juan Migliore, Rosa M. Miró-Roig, Satoshi Murai*, Uwe Nagel, Junzo Watanabe

*この研究の対応する著者

研究成果: Article査読

2 被引用数 (Scopus)

抄録

A homogeneous ideal I of a polynomial ring S is said to have the Rees property if, for any homogeneous ideal J ⊂ S which contains I, the number of generators of J is smaller than or equal to that of I. A homogeneous ideal I ⊂ S is said to be m-full if mI:y=I for some y ∈ m, where m is the graded maximal ideal of S. It was proved by one of the authors that m-full ideals have the Rees property and that the converse holds in a polynomial ring with two variables. In this note, we give examples of ideals which have the Rees property but are not m-full in a polynomial ring with more than two variables. To prove this result, we also show that every Artinian monomial almost complete intersection in three variables has the Sperner property.

本文言語English
ページ(範囲)445-454
ページ数10
ジャーナルArchiv der Mathematik
101
5
DOI
出版ステータスPublished - 2013 11
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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