… of modules which satisfy the conditions 𝒬 ′ ⊆𝒬, 𝒬 ∩ ℛ = 𝒬 ′ ∩ ℛ ′ , and ℛ ′ is enveloping,
a kind of Tate homology T o r ̂ ∗ 𝒬 ℳ of modules … Three aspects of applications for the …

… of semidualizing modules to a pair of non-commutative, but Noetherian rings. Furthermore,
Holm and White in [21] generalized the notion of a semidualizing module … many homological …

… (non-necessarily semidualizing) left R-module C, we introduce … homological dimension with
respect to a semidualizing … the class of flat modules forms the left side of a perfect cotorsion …

… In [4], Fossum et al. studied the categorical aspect and homological properties of the
trivial … RM-modules when R is a commutative Noetherian ring and M is a semi-dualizing R-module. …

… generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander
and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre’s …

… C -resolutions, for convenience we use just lengths of exact sequences of modules in 𝒫 C .
However, as in the case of semidualizing modules [4], later in this section (Theorem 2.11) we …

… homological dimensions. In summary, these classes are powerful tools for studying homological
dimensions of modules … a priori require C to be semidualizing. However, when C is not …

… The purpose of this paper is to survey recent algebraic and homological properties of the …
In this paper, we survey briefly recent algebraic and homological properties of the …

… rings and S VR a semidualizing (S-R)-bimodule. An R-… of modules of finite V-Gi-injective
dimension and by using it we will prove that vanishing of the relative homological modules Ext …

… that if a semidualizing module C has a canonical module and belongs … side is isomorphic
to HomR(N,ωC) ⊗R R/xR. Again by [4, Proposition 3.3.3], we conclude that the right-hand side …