In this paper we study homological dimensions of finitely generated modules over
commutative Noetherian local rings, called reducing homological dimensions. We obtain …

Let $\Lambda $ be a left and right Noetherian ring. First, for $ m, n\in\mathbb {N}\cup\{\infty\}
$, we give equivalent conditions for a given $\Lambda $-module to be $ n $-torsionfree and …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from 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 …

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

Motivated by a recent result of Yoshino and the work of Bergh on reducible complexity, we
introduce reducing versions of invariants of finitely generated modules over local rings. Our …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary
ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein
homological dimensions of rings. Also, we study the Gorenstein homological dimensions of …

The classical global and weak dimensions of rings play an important role in the theory of
rings and have a great impact on homological and commutative algebra. In this paper, we …