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) …

Let R denote a commutative Noetherian (not necessarily local) ring, 𝔞 an ideal of R and M a
finitely generated R-module. The purpose of this article is to show that for any finitely …

Let (R, m) denote a local Cohen–Macaulay ring and I a non-nilpotent ideal of R. e purpose
of this article is to investigate Faltings' niteness dimension fI (R) and the …

Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M a non-zero finitely
generated R-module. Let t be a non-negative integer. In this paper, it is shown that for all i< t …

Let R denote a commutative Noetherian ring, aa an ideal of R, and M an a a-cofinite R-
module. The purpose of this article is to show that for a positive integer t, the R-module H …

Let (R, 𝔪) be a complete local ring, 𝔞 an ideal of R, and M a finitely generated R-module.
The aim of this paper is to show that for any non-negative integer n,, where is the n th …

Let be an ideal of a commutative Noetherian ring R, and let M and N be finitely generated R-
modules. Let be the-finiteness dimension of N. In this paper, among other things, we show …

Throughout R is a commutative Noetherian ring with nonzero identity, a is an ideal of R, and
n is a nonnegative integer. We write Spec (R)≥ n={p∈ Spec (R): dim (R/p)≥ n}, AssR (X)≥ …

Let (R, m) be a commutative Noetherian local ring, I an ideal of R and let M be a non-zero I-
cofinite R-module. In this paper we show that if M has finite injective dimension, then dim …

Throughout, R is a commutative Noetherian ring with non-zero identity, a is an ideal of R, M
is a finite (ie, finitely generated) R-module, and n is a non-negative integer. For basic results …