We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …

Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …

Let $ R $ be a commutative noetherian local ring, and let $ M $ be a finitely generated $ R $-
module. Inspired by works of Vasconcelos and Briggs on characterization of complete …

Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a
semidualizing module to be dualizing in terms of special homological properties of module …

Let $ R $ be a Noetherian local ring, and let $ C $ be a semidualizing $ R $-module. In this
paper, we present some results concerning to vanishing of $\operatorname {Ext} $ and finite …

Let R and S be rings and _SC_R a faithfully semidualizing bimodule. A left S-module M is
called Ding C-projective if there exists an exact sequence of C-projective left S-modules …

Let S and R be rings, SCR be a semidualizing bimodule and n≥ 0 be an integer or n=∞.
We introduce and study C-FP n-injective and C-FP n-flat modules as a common …

Let R and S be rings and SCR a semidualizing bimodule. We investigate the relative Tor
functors Tor i ℳ ℒ C (−,−) Tor_i^ML_C(-,-) defined via C-level resolutions, and these functors …

Let $ R $ be a commutative Noetherian local ring and $ M $ a finitely generated $ R $-
module. We introduce a general form of the classically studied trace map that unifies several …

arXiv:2312.06124v1 [math.AC] 11 Dec 2023 Page 1 arXiv:2312.06124v1 [math.AC] 11 Dec
2023 SOME RESULTS ON VANISHING OF EXT AND FINITE GORENSTEIN DIMENSION OF …