Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4596664 | Journal of Pure and Applied Algebra | 2014 | 15 Pages |
Abstract
Let (R,m) be an analytically unramified Cohen-Macaulay local ring of dimension 2 with infinite residue field and I¯ be the integral closure of an ideal I in R. Necessary and sufficient conditions are given for Ir+1Js+1¯=aIrJs+1¯+bIr+1Js¯ to hold for all r⩾r0 and s⩾s0 in terms of vanishing of [H(at1,bt2)2(Râ²Â¯(I,J))](r0,s0), where aâI,bâJ is a good joint reduction of the filtration {IrJs¯}. This is used to derive a theorem due to Rees on normal joint reduction number zero. The vanishing of e¯2(IJ) is shown to be equivalent to Cohen-Macaulayness of R¯(I,J).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shreedevi K. Masuti, J.K. Verma,