Sequentially Cohen-Macaulayness versus parametric decomposition of powers of parameter ideals

Cohen-Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals

“…We close this section with an application to sequentially Cohen-Macaulay rings. We refer the reader to [6] for the definition and details. See also [2,14,15].…”

“…Let U = U A (0). In the notation of Proposition 3.14, we have that t 2 and M t−1 = U (see [6,Theorem 2.3]). Therefore dim U d − 2, since dim A/p = d − 1 for all p ∈ Ass(A).…”

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

“…Let M be a finitely generated A-module. We say that M is a sequentially Cohen-Macaulay A-module, if M possesses a Cohen-Macaulay filtration, that is a filtration 4,12,26,28]).…”