In this paper, we introduce and study left (right) G-hereditary rings over any associative ring,
and these rings are exactly G-hereditary rings defined by Mahdou and Tamekkante provided …

In this paper, we introduce and study left (right) G-semihereditary rings over any associative
ring, and these rings are exactly G-semihereditary rings defined by Mahdou and …

A ring R is called Gorenstein hereditary (G-hereditary) if every submodule of a projective
module is Gorenstein projective (ie Ggldim (R)≤ 1). In this paper, we settle a question …

Rings of invariants can have nice homological properties even if they do not have finite
global dimension. Watanabe's Theorem [W] gives conditions when the fixed subring of a …

A noncommutative generalization of Auslander′s last theorem Page 1 A
NONCOMMUTATIVE GENERALIZATION OF AUSLANDER’S LAST THEOREM EDGAR E …

In this note, we mainly discuss strongly Gorenstein hereditary rings. We prove that for any
ring, the class of SG-projective modules and the class of G-projective modules coincide if …

The study of rings and modules with homological criteria is a cornerstone of commutative
algebra. Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and …

In this paper, we investigate the properties of right orthogonal modules of CC, where CC is a
class of left R-modules. As an application, we investigate the properties of right orthogonal …

Let R be a commutative Noetherian ring. In this paper, we study those finitely generated R-
modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a …

It is well known that the decomposition of injective modules over Noether rings and the
decomposition of projective modules over Artinian rings are some of the most beautiful and …