Super height of an ideal in a Noetherian ring
type: Item
instance of: scholarly article
title: Super height of an ideal in a Noetherian ring
zbMATH Open document ID: 0655.13012
DOI: 10.1016/0021-8693(88)90194-9
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The aim of this paper is to prove the following two results: Theorem 1: Let R be a commutative finitely generated algebra over a field and let P be a prime ideal of R. Then: super ht IR\(_ P=\) finite super ht IR\(_ P\) for all ideals I of R contained in P. - Theorem 2: Let p be a prime integer, \(F_ p\) the algebraic closure of \({\mathbb{Z}}/p{\mathbb{Z}}\), \(V_ p\) the ring of Witt vectors over \(F_ p\), and R a commutative finitely generated algebra over \(V_ p\). Then: super ht I=finite super ht I for all ideals I of R. Recall that if I is an arbitrary ideal in a Noetherian ring R, then super ht I (resp. finite super ht I)\(=\) \(\sup \{ht(IS)| \quad IS\neq S,\) S is a Noetherian (resp. S is a finitely generated) R-algebra\}.
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 4069038
zbMATH Keywords: finite super height of an ideal
zbMATH Keywords: henselization
zbMATH Keywords: Witt vectors
author: Jee Koh
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90194-9
OpenAlex ID: W2002800379
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description: scientific article; zbMATH DE number 4069038