On the embedded primary components of ideals. II
type: Item
instance of: scholarly article
title: On the embedded primary components of ideals. II
zbMATH Open document ID: 0853.13001
DOI: 10.1016/0022-4049(94)00018-E
author: Louis J. Ratliff
author: Kishor Shah
author: William J. Heinzer
published in: Journal of Pure and Applied Algebra
publication date: 1996-12-12T00:00:00Z
review text: This paper is the second one in a series of four papers where the authors study embedded primary components of ideals [Part I: J. Algebra 167, No. 3, 724-744 (1994); part III: ibid. 171, No. 1, 272-293 (1995); part IV: Trans. Am. Math. Soc. 347, No. 2, 701-708 (1995); see respectively: Zbl 0822.13001; Zbl 0822.13002; and Zbl 0822.13003)]. Let \((R, {\mathfrak m})\) be a local Noetherian ring and \(I\) an ideal in \(R\) such that \({\mathfrak m}\) is an embedded prime of \(I\). Then the authors introduced the concept of of MEC (= maximal embedded component) of \(I\). This is a primary component of \(I\) which is maximal among all embedded \({\mathfrak m}\)-primary components. The authors study the question when a given ideal is a MEC of an ideal \(I\) and give various characterization of MEC's. In particular it follows that not every \({\mathfrak m}\)-primary ideal occurs as a MEC. The authors also examine the close connection with ideal covers.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13H99
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 802556
zbMATH Keywords: primary decomposition
zbMATH Keywords: embedded primary components of ideals
zbMATH Keywords: maximal embedded component
zbMATH Keywords: ideal covers
reviewed by: Hubert Flenner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 802556