Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the
projective and injective dimensions of a finite module $ M $ over a (commutative) …

For finite modules over a local ring and complexes with finitely generated homology, we
consider several homological invariants sharing some basic properties with projective …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

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

GORENSTEIN DIMENSIONS MODULO A REGULAR ELEMENT Page 1 J. Aust. Math. Soc. 99
(2015), 260–266 doi:10.1017/S1446788714000871 GORENSTEIN DIMENSIONS MODULO A …

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 commutative Noetherian local ring. It is known that R is Cohen–Macaulay if
there exists either a nonzero finitely generated R-module of finite injective dimension or a …

Let (R, m) be commutative Noetherian local ring. It is shown that R is Cohen-Macaulay ring if
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …

We search for some splitting (resp. finiteness) criteria of a given module $ M $ over a local
ring $(R,\fm, k) $ in terms of the splitting (resp. finiteness) property of certain cohomological …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …