In this note, we introduce a homological invariant for finitely generated modules over
commutative noetherian local rings by slightly modifying the definition of complete …

Let A be a noetherian local ring, I an ideal of A, and B= A/I. In this paper we deal with the
relationship among the finiteness of the complete intersection dimension of the A-module B …

Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …

In this paper, we are concerned with certain invariants of modules, called reducing
invariants, which have been recently introduced and studied by Araya–Celikbas and Araya …

A new homological invariant is introduced for a finite module over a commutative noetherian
ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained …

The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension
codim (End (MR)) of the endomorphism ring End (MR) of a module MR can be used as a …

This chapter discusses a commutative noetherian local ring with maximal ideal and residue
field. The local ring has sometimes a canonical module, which is of great significance, even …

We prove that if f: R→ S is a local homomorphism of noetherian local rings, and M is a non-
zero finitely generated or artinian S-module whose injective dimension over R is bounded …

Let (R, m) be a commutative Noetherian local ring, I a proper ideal of R and M a finitely
generated R-module of dimension d. We investigate Falting's finiteness dimension f I (M) …

In this paper we are concerned with certain invariants of modules, called reducing
invariants, which have been recently introduced and studied by Araya-Celikbas and Araya …