On a class of modules

Creative Commons License

Ozcan A. Ç.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.57, pp.269-275, 2000 (SCI-Expanded) identifier identifier identifier


Let R be a ring with identity and M a unital right R-module. Let Z*(M) = {m epsilon M : mR << E(mR)}. In this study we consider the property (T): For every right R-module M with Z*(M) = Rad M, M is injective. We give a characterization of the property (T) when R is a prime PI-ring. Also, over a right Noetherian ring R we prove that if R satisfies (T) then every right R-module is the direct sum of an injective module and a Max-module.