In this article, we shall characterize torsionfreeness of modules with respect to a
semidualizing module in terms of the Serre's condition (Sn). As an application we give a …

For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules
is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

Let R be an associative ring with identity. An (left) R-module M is said to be torsion if for
every m∈ M, there exists a nonzero r∈ R such that rm= 0, and faithful provided rM={0} …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

Let R be a commutative (possibly non-Noetherian) ring (in order to make things less
technical) and C a semidualizing R-module. In this article, we introduce and investigate the …

In this paper, we study the pair (GP(R),GP(R)^⊥) where GP(R) is the class of all Gorenstein
projective modules. We prove that it is a complete hereditary cotorsion theory, provided …

We contribute to the theory of G-dimension relative to a semidualizing module C, in
connection to the properties of a module being totally C-reflexive, Ck-torsionless, and Ck …

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …

We generalize the homological characterization of sequentially Cohen–Macaulay modules
over a graded Gorenstein algebra to sequentially reflexive modules over Noetherian, not …