  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 Knoerrer
periodicity for Gorenstein flat modules is developed.
