Semidualizing modules and trivial ring extensions

Abstract

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 if and only if T(C) is a semidualizing R ⋉ M-module and Tor_i^R(C,M) = 0 for any i ≥ 1. Finally, we describe when T(C) is a dualizing R ⋉ M-module.