… to construct new semidualizing modules from given semidualizing modules via trivial
extensions of rings. To this end, in Section 2, we first investigate some homological properties over …

… -module formed by the K-derivations of R, ie, the elements of … a canonical module ωR, then
ωR is semidualizing. Also recall … Let C be a semidualizing R-module. Then, R is regular if and …

… 3 we study the homological dimensions associated to … /J goes from the right side to the left
side of the short exact sequence. … definition of a semidualizing module for a Noetherian ring R. …

… Fossum, Griffith and Reiten studied the categorical aspect and homological properties of
trivial … Jørgensen: Semi-dualizing modules and related Gorenstein homological dimensions. J. …

… As the second application of Corollary 3.6, using a result of Herzog about trivial extension,
we give a characterization of local rings that admit non-trivial semidualizing module; see …

… on the structure and homological properties of these rings, … A dualizing complex for φ is a
semidualizing S-complex D φ … G ] ] out by the regular sequence of elements of the form v i , j − w …

… of homology modules. Fix an integer i and note that \({\text {H}}_i (M^{\ell }) =0\) if \… elements
of J are not all of the form of a monomial, so to define the “powers” of non-monomial elements …

… Among various research areas on semidualizing modules, one basically focuses on … and
results of homological algebra to the relative setting with respect to a semidualizing module. For …

… It is known that every homological dimension of modules is defined relative to some … of
semidualizing bimodules include the free module of rank one and the dualizing module over a …

… semidualizing modules and related modules; see [6–17], and so on. Among various research
areas on semidualizing modules… “absolute” classical results in homological algebra to the “…