Let M be a finitely generated module over a Noetherian local ring (R, m) with dimM= d. Let
(x1,…, xd) be a system of parameters of M and (n1,…, nd) a set of positive integers …

Let be a Noetherian local ring and let M be a finitely generated R-module of dimension d.
Let be a system of parameters of M and let be a d-tuple of positive integers. In this paper we …

Throughout this paper, let M be a finitely generated module over a Noether local ring
(A,[mfr]) with dim M= d. Let x=(x1,…, xd) be a system of parameters of M and n=(n1,…, nd)∈ …

Throughout, let A be a (commutative Noetherian) local ring (with identity) of dimension d> 0,
having maximal ideal m. For an m-primary ideal q of A, we shall denote the multiplicity of q …

The purpose of this paper is to provide additional evidence to support our view that the
modules of generalized fractions introduced in [8] are worth further investigation: we show …

We consider several multiplicity functions associated with a pair of ideals J⊆ I in a local
noetherian ring R. In particular, given an arbitrary ideal J and an element x∈ R, we show …

We introduce the notion of strict f-sequence and apply this concept to study the finiteness of
asymptotic sets of attached prime ideals of local cohomology modules of M, to study the …

Let (R, m, k) be a d-dimensional Noetherian reduced local ring of prime characteristic p such
that [Formula: see text] are finite over R for all e∈ N (ie R is F-finite). Consider the sequence …

Let $(R, M) $ be a local ring with infinite residue field and $ I=({x_1},\ldots,{x_d}) R $ an ideal
generated by a system of parameters. It is shown that the multiplicity of $ I $ equals the …

Throughout this paper, let A be a Noetherian local ring with maximal ideal m and M a finitely
generated A-module with d= dimAM≥ 1. Denote by N the set of all positive integers. Let …