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 …

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 …

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)∈ …

Let R be a ring with non-zero identity and unitary left R-modules, while N _R is the
subcategory of Noetherian R-modules. Given a length function L on N _R and central …

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 …

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 …

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 …

Introduction THE present paper generalizes some results in the multiplicative theory of
fractional ideals. To be explicit, let R be a one-dimensional local ring and M its maximal …

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 …

Introduction. In this paper we shall introduce a theory of length for Nartherian modules over
an arbitrary ring (with identity), assigning to each Noetherian module M an ordinal number l …