In this article, we prove that Gorenstein projectivity and injectivity with respect to a
semidualizing module are preserved under Frobenius extensions. Furthermore, we obtain …

The classes of GC homological modules over commutative ring, where C is a semidualizing
module, extend Holm and J gensen's notions of C-Gorenstein homological modules to the …

In this paper, let R be a commutative ring and C a semidualizing module. We investigate the
(weak) C-Gorenstein global dimension of R and we get a simple formula to compute the C …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …

Let C be a semidualizing module for a commutative ring R. In this paper, we study the
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …

Let R be a commutative Noetherian ring. The aim of this paper is studying the properties of
relative Gorenstein modules with respect to a dualizing module. It is shown that every …

Abstract Let R⊂ S be a Frobenius extension of rings and M an S-complex. It is proven that if
the Gorenstein projective (injective) dimension of M as an S-complex is finite, then the …

Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is proved
that FPD (R)= sup {GPC− pd R (M)| M∈ BC (R) and GPC− pd R (M)<∞}, which is a …

In this article, we study finite Gorenstein homological dimensions of complexes with respect
to a semidualizing module. A special attention is paid to the dimensions of homologically …

ABSTRACT Let R⊂ A be a Frobenius extension of rings. We prove that:(1) for any left A-
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …