On the embedded primary components of ideals. II
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.
scientific article; zbMATH DE number 802556