Let R be a ring, and M a bimodule over R. The trivial extension R x M is as abelian group
R@ M and the multiplication is given by (I, m)(r', m')=(rr', rm'+ mr'). Palmer and Roos give in …

Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving
subcategory of finitely generated R-modules. This paper mainly studies when X contains k …

Let (R, m) be a local ring, and let C be a semidualizing R-module. In this paper, we are
concerned with the C-injective and GC-injective dimensions of certain local cohomology …

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 …

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if
there exists either a nonzero finitely generated R-module of finite injective dimension or a …

In the last few years, López-Permouth and several collaborators have introduced a new
approach in the study of the classical projectivity, injectivity and flatness of modules. This …

Acta Mathematica Sinica, English Series Page 1 Acta Mathematica Sinica, English Series
Nov., 2017, Vol. 33, No. 11, pp. 1513–1535 Published online: July 15, 2017 https://doi.org/10.1007/s10114-017-6416-8 …

For finitely generated modules $ M $ and $ N $ over a commutative Noetherian local ring $
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …

Let R be a commutative Noetherian ring, I an ideal of R and M an arbitrary R-module. Let S
be a Serre subcategory of the category of R-modules. It is shown that the R-module …

Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …