Record Details


Field	Value

Title	Bounds on the a-invariant and reduction numbers of ideals

Creator	D'CRUZ, C KODIYALAM, V VERMA, JK

Subject	a-invariant reduction number eisenbud-goto invariant local cohomology

Description	Let R be a d-dimensional standard graded ring over an Artinian local ring. Let M be the unique maximal homogeneous ideal of R. Let h(i) (R), denote the length of the nth graded component of the local cohomology module H-M(i)(R). Define the Eisenbud-Goto invariant EG(R) of R to be the number Sigma(q=0)(d-1) ((d-1)(q))h(M)(q)(R)(1-q). We prove that the a-invariant a(R) of the top local cohomology module H-M(d) (R) satisfies the inequality: a(R) less than or equal to e(R) - l(R-1) + (d - 1)(l(R-0) - 1) +EG(R). This bound is used to get upper bounds for the reduction number of an m-primary ideal I of a Cohen-Macaulay local ring (R, m), when the associated graded ring of I has depth at least d - 1. (C) 2004

Publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE

Date	2011-07-12T14:27:17Z 2011-12-26T12:48:56Z 2011-12-27T05:34:27Z 2011-07-12T14:27:17Z 2011-12-26T12:48:56Z 2011-12-27T05:34:27Z 2004

Type	Article

Identifier	JOURNAL OF ALGEBRA, 274(2), 594-601 0021-8693 http://dx.doi.org/10.1016/j.jalgebra.2003.12.007 http://dspace.library.iitb.ac.in/xmlui/handle/10054/3351 http://hdl.handle.net/10054/3351

Language	en

ICAR Research Data Repository for Knowledge Management