Purity and ascent for Gorenstein Flat Cotorsion modules

Abstract

The extension of scalars functor along a finite ring homomorphism is a classic example of a functor which preserves purity and pure injectivity. We consider how this functor behaves when restricted to the class of Gorenstein flat modules over a right coherent rings, and give particular attention to the Frobenius category of Gorenstein flat and cotorsion modules by showing there is an induced triangulated functor on the stable categories. This enables a comparison between pure injectivity for Gorenstein flat modules and pure injectivity in the triangulated categories as well as an investigation in how purity for Gorenstein flat modules is transferred along the homomorphism. Throughout motivating examples from commutative algebra are considered, including over hypersurfaces where a pure injective analogue of Knörrer periodicity for Gorenstein flat modules is developed.

Finiteness properties and homological dimensions of Skew Group rings

“…Since the functor RG⊗ R − preserves modules that are simultaneously Gorestein flat and cotorsion by [42, Propositions 2.3 and 2.5]; after a direct application of [8,Theorem 3.3] and Proposition 3.5 we get the following result. 8.1.…”