Uniform Modules Over Goldie Prime Serial Rings

Abstract

We investigate the uniseriality of uniform injective modules over serial rings. Let R be an arbitrary ring and fix a decomposition, of the identity, 1 = e ₁ + e ₂ + ⋯ + e _n into orthogonal idempotents. For any uniform injective module V _R , we prove that there exists e = e _i such that, with A = eRe, V _R ≅ hom _A (Re,Ve). Moreover, Ve is a uniform injective A-module. We also show that if R is Goldie prime serial, then V is uniserial if and only if Ve is uniserial as an A-module.