On Hulls of Semiprime Rings

Abstract

Suppose R is a unital ring with a ring of quotients. We construct an intermediate ring between R and the maximal right ring of quotients Q(R). The intermediate ring lies in a class of rings that generalizes the class of self-injective rings, it is a right ring hull of R and it is a right pseudo ring hull of R. Properties about nilpotency and regularities of rings are shown to be transferred between a semiprime ring and this hull which is FI-extending and at the same time quasi-Baer. A counter example is given to show that transference of properties between any R and Q(R) does not take place in general.