On Maximal Torsion Radicals

Abstract

Let R be an associative ring with identity, and let denote the category of unital left R-modules. It is known that if R is a commutative, Noetherian ring, then the maximal torsion radicals of correspond to the minimal prime ideals of R. In fact, Nӑstӑsescu and Popescu [15, Proposition 2.7] have given a more general result valid for arbitrary commutative rings. This paper investigates maximal torsion radicals over rings not necessarily commutative.