Right Utumi P.P.-Rings

Abstract

The class of right Utumi p.p.-rings plays a central role when developing a notion of torsion-freeness over non-commutative rings. This paper shows that it also arises naturally when considering divisible modules. Various notions of divisibility were introduced for modules over integral domains. We determine their relation in the non-commutative case and show that there are significant differences between this and the commutative setting. Finally, we determine large classes of semi-prime Goldie rings for which two or more of these notions coincide.