Stability of Gelfand–Kirillov dimension for rings with the strong second layer condition

Abstract

We study the influence of the link structure of the prime spectrum of a Noetherian ring on the representation theory of the ring in the case that the ring satisfies the strong second layer condition and has exact integer Gelfand–Kirillov dimension. In particular, we show that Jategaonkar's density condition is satisfied and that the growth of an injective module is controlled by the growth of its first layer.