Let $R$ be a left noetherian ring, then it is well known that Matlis proved that any injective $R$-module decomposes into a sum of indecomposable injectives, each of form $E(R/I)$ for some irreducible left ideal $I$. If moreover $R$ is commutative, we know much more: indecomposable injectives correspond to prime ideals via $P \rightarrow E(R/P)$ and each $E(R/P)$ is filtered by vector spaces over quotient field of $R/P$, which makes it quite analogical to injective abelian groups in my eyes.

What is known in the non-commutative case? Is there also some nice filtration as in the commutative case?

Thanks in advance for any reference.