Gorenstein Associated Graded Rings of Analytic Deviation Two Ideals

Abstract

This paper studies the question of when the associated graded ring I = n≥0 I n /I n+1 of a certain ideal I in a local ring is Gorenstein. The main result implies, for example, that if A is a regular local ring, is a prime ideal in A with dim A/ = 2, and A/ is a complete intersection in codimension one, then the associated graded ring is Gorenstein if and only if the reduction number of is at most 1.  2002 Elsevier Science (USA)

Gorenstein graded rings associated to ideals

“…We can find references analyzing mixed ideals, whereas its analytic deviation is at most 2 (cf. [8][9][10]). For the case where n = 1, the first author, Nakamura, and Nishida [13] gave a characterization on the Gorensteinness of G(I ) in the case where ad(I ) = 1.…”