Buchsbaumness in local rings possessing constant first Hilbert coefficients of parameters

Variation of the first Hilbert coefficients of parameters with a common integral closure

“…and call it the Sally module of I with respect to Q ( [32]). Sally modules play a very important role in the analysis of ideals I with interaction to their reductions Q (see, e.g., [15,16,18]), as we will also see in the following. where m denotes the maximal ideal of A and x, y, z, and w denote the images of X, Y, Z, and W in A respectively.…”

“…Lemma 2.4]) and[18, Theorem 2.1]. See[5, Theorem 2.1] for the inequality0 > e 1 Q ′ (A).Let us construct counterexamples.…”

The Chern Numbers and Euler Characteristics of Modules

“…We begin with the following two results, whose proofs are similar to those in the ring case (see [8,Lemma 4.5] and [13,Proposition 2.3]).…”

“…We establish here that if e 1 (Q, M ) is constant and M is unmixed, then M is indeed a Buchsbaum R-module (Theorem 5.4). See [13] for the ring case.…”

“…The authors have examined ( [8], [9], [13], [32]) how the values of e 1 (Q, R) codes for structural information about the ring R itself. More explicitly one defines the set…”