  In this paper we investigate injective generation for graded rings. We first
examine the relation between injective generation and graded injective
generation for graded rings. We then reduce the study of injective generation
for graded rings to the study of injective generation for certain Morita
context rings and we provide sufficient conditions for injective generation of
the latter. We then provide necessary and sufficient conditions so that
injectives generate for tensor rings and for trivial extension rings. We
provide two proofs for the class of tensor rings, the one uses covering theory
and the other uses the framework of cleft extensions of module categories. We
finally prove injective generation for twisted tensor products of finite
dimensional algebras.
