Idealizations of maximal Buchsbaum modules over a Buchsbaum ring

Abstract

Throughout this paper A denotes a Noetherian local ring with maximal ideal m and M denotes a finitely generated A-module. Moreover stands for the ith local cohomology functor with respect to m (cf. [10]). We refer to [15] for unexplained terminolog.

Buchsbaumness of certain generalization of the associated graded modules in the equi-I-invariant case

“…IV], this system is extended to the required one immediately, cf. see also [Y1,Remark (5) a 1 , a 2 , . .…”

“…Though the injectivity of ( 4.3) is coming from similar arguments as in the proof of [Y1,Theorem 4.1], we shall here discuss it quickly for reader's convenience. Via…”

Buchsbaumness in Rees Modules Associated to Ideals of Minimal Multiplicity in the Equi-I-Invariant Case

“…Therefore, the Rees algebra R is Buchsbaum by Theorem 1.1. For instance, if A possesses the canonical module K A and if the idealization A K A is a Buchsbaum ring, then by [Y1,Theorem 3.3] the -primary ideal = satisfies the equality 2 = . On the other hand, according to [CP,Theorem 2.2], if A is a Cohen-Macaulay local ring which is not a regular local ring, the -primary ideal = satisfies the equality 2 = .…”

The associated graded modules of Buchsbaum modules with respect to m-primary ideals in the equi-II-invariant case

“…In fact, the assertion (2.2) (resp. (2.4)) is given in the same way as in the proof of [Y,Lemma 1.2] (resp. [G2, Corollary(1.2)]), and see also [GY,Theorem (2.3) and Theorem (2.6)] for more explicit statements.…”