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 …

On Vanishing of Generalized Local Cohomology Modules Page 1 Algebra Colloquium c© 2005
AMSS CAS & SUZHOU UNIV Algebra Colloquium 12:2 (2005) 213–218 On Vanishing of …

Let R be a commutative noetherian henselian non-Gorenstein local ring. The author has
conjectured in [R. Takahashi, On the category of modules of Gorenstein dimension zero …

The main aim of this paper is to obtain a dual result to the now well known Auslander-
Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring …

The starting point for the discussion in the present paper is another result of Levin and
Vasconcelos. In [13], Theorem 2.2, they proved that, if R is a Gorenstein local ring, then a fg …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

In this paper, we study Gorenstein projective and flat modules over a Noetherian ring R. For
an R-module M, we show that Gorenstein projective dimension of M is finite if and only if …

Let A be a commutative local Noetherian ring with identity of Krull dimension n, m its
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …

For a Noetherian ring $ R $ we call an $ R $-module $ M $ cofinite if there exists an ideal $ I
$ of $ R $ such that $ M $ is $ I $-cofinite; we show that every cofinite module $ M $ satisfies …

In this paper, we continue the study of cominimaxness modules with respect to an ideal of a
commutative Noetherian ring (cf.\cite {ANV}), and Bass numbers of local cohomology …