Lattice-ordered modules of quotients

Abstract

Let Q be the ring of quotients of the/-ring R with respect to a positive hereditary torsion theory and suppose Q is a right/-ring. It is shown that if the finitely-generated right ideals of R are principal, then Q is an/-ring. Also, if Q R is injective, Q is an/ring if and only if its Jacobson radical is convex. Moreover, a class of po-rings is introduced (which includes the classes of commutative po-rings and right convex/-rings) over which Q(M) is an /-module for each/-module M.