Article ID Journal Published Year Pages File Type
4587927 Journal of Algebra 2008 11 Pages PDF
Abstract

The purpose of this paper is to give affirmative answers to two open questions as follows. Let (R,m) be a generalized Cohen–Macaulay Noetherian local ring. Both questions, the first question was raised by M. Rogers [M. Rogers, The index of reducibility for parameter ideals in low dimension, J. Algebra 278 (2004) 571–584] and the second one is due to S. Goto and H. Sakurai [S. Goto, H. Sakurai, The equality I2=QI in Buchsbaum rings, Rend. Sem. Mat. Univ. Padova 110 (2003) 25–56], ask whether for every parameter ideal q contained in a high enough power of the maximal ideal m the following statements are true: (1) The index of reducibility NR(q;R) is independent of the choice of q; and (2) I2=qI, where I=q:Rm.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory