Let $ R $ be a ring with Gwgldim $(R)<\infty $. We obtain a triangle-equivalence $\mathrm
{K}(R\text {-}\mathrm {GProj})\simeq\mathrm {K}(R\text {-}\mathrm {GInj}) $ which restricts to a …

Given a group G acting on a ring R, one can form the skew group ring R∗ G. We give
conditions for a von Neumann regular skew group ring to be simple. We use this information …

For a class of $ R $-modules $\mathcal {X} $ containing all projective $ R $-modules, the
$\mathcal {X} $-Gorenstein projective $ R $-modules vary from projective to Gorenstein …

Let R be a left and right ℵ0-Noetherian ring. We show that if all projective left and all
projective right R-modules have finite injective dimension, then all injective left and all …

In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …

Chapter 17 Wakamatsu Tilting Modules, U-Dominant Dimension, and k-Gorenstein Modules
Zhaoyong Huang Department of Mathematics, Nanjing University, Nanjing 210093, People's …

We construct simple Noetherian rings S of characteristic p, for any prime p, such that S has
zero divisors but no non-trivial idempotents, and S is not Morita equivalent to a domain. Our …

A ring is called $ n $-perfect ($ n\geq 0$), if every flat module has projective dimension less
or equal than $ n $. In this paper, we show that the $ n $-perfectness relate, via homological …

It is well known that a ring R is right Kasch if each simple right R-module embeds in a
projective right R-module. In this paper we study the dual notion and call a ring R right dual …

In this paper, we consider partial actions of groups on rings and invariant subrings under
partial actions. After some general results we study the transference of properties from …