Upper complete intersection dimension relative to a local homomorphism
type: Item
instance of: scholarly article
title: Upper complete intersection dimension relative to a local homomorphism
zbMATH Open document ID: 1058.13009
author: Ryo Takahashi
published in: Tokyo Journal of Mathematics
publication date: 2005-01-04T00:00:00Z
review text: Recently many authors studied new homological invariants: complete intersection dimension, Gorenstein dimension and others. They have similar properties as projective dimension. In the present paper, the author adds one more new invariant, called upper complete intersection dimension relative to a local homomorphism, to the sequence of homological invariants above. Let \(R\) be a Noetherian local ring and \(M\) a finitely generated \(R\)-module. The complete intersection dimension and others are integers (or symbol \(\infty\)) assigned to~\(M\). However, the relative upper complete intersection dimension is assigned to the pair of~\(M\) and a local homomorphism \(\phi \: S \to R\), where \(S\) is another Noetherian local ring. It properly depends on the choice of~\(\phi\). It is possible that the relative upper complete intersection dimension has more information of~\(M\) than other homological dimensions.
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 13D22
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13C40
zbMATH DE Number: 2124829
zbMATH Keywords: upper complete intersection dimension
zbMATH Keywords: local homomorphism
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208485
OpenAlex ID: W2002361210
DOI: 10.3836/TJM/1244208485
description: scientific article; zbMATH DE number 2124829