Semidualizing modules and trivial ring extensions

Let R M be a trivial extension of a commutative ring R by an R-R-bimodule M. We first investigate some homological properties over R M. Then we provide a way to construct new semidualizing R M-modules from given semidualizing R-modules. It is proven that C is a semidualizing R-module and M belongs to the Auslander class AC(R) if and only if T(C) is a semidualizing R M-module and TorᵢR(C,M) = 0 for any i ≥ 1. Finally, we describe when T(C) is a dualizing R M-module.