Krull dimension and monomial orders

JOURNAL OF ALGEBRA

卷:399

Article

Kemper, Gregor¹  Ngo Viet Trung² 

[1] Tech Univ Munich, Zentrum Math M11, D-85748 Garching, Germany

[2] Vietnam Acad Sci & Technol, Inst Math, Hanoi 10307, Vietnam

关键词: Krull dimension;    Weight order;    Monomial order;    Independent sequence;    Analytically independent;    Associated graded ring;    Jacobson ring;    Subfinite algebra;   

DOI  :  10.1016/j.jalgebra.2013.10.005

来源: Elsevier

【 摘 要 】

We introduce the notion of independent sequences with respect to a monomial order by using the least terms of polynomials vanishing at the sequence. Our main result shows that the Krull dimension of a Noetherian ring is equal to the supremum of the length of independent sequences. The proof has led to other notions of independent sequences, which have interesting applications. For example, we can show that dim R/0 : J(infinity) is the maximum number of analytically independent elements hi an arbitrary ideal J of a local ring R and that dim B <= dim A if B subset of A are (not necessarily finitely generated) subalgebras of a finitely generated algebra over a Noetherian Jacobson ring. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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