The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-
Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

Let (R, m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be
a finite R-module and t an integer between 0 and d. If the GC-dimension of M/aM is finite for …

We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …

Let R be a commutative Noetherian ring with identity, I be an ideal of R and M, N be two R-
modules. Throughout this paper, we denote by idR M and fdR M the injective dimension and …

In the last time, several papers concerning the homological dimensions of rings have
appeared in the literature. Among others, C. Nastasescu [lo] has shown that for a …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Let $ R $ be a commutative noetherian local ring and denote by $\operatorname {mod} R $
the category of finitely generated $ R $-modules. In this paper, we give some evaluations of …

Then 6 (R) is also equal to sup {id (M)(M is a cocyclic left R module}. Ot course the
homological invariant 6 (R) is< gld (R). For a commutative ring R it is easy to prove that 6 …

It is well known that the right global dimension of a ring R is usually computed by the right
derived functors of Hom and the left projective resolutions of right R-modules. In this paper …