This book is an account of a certain portion of noncommutative ring theory which originated
in the work of RE Johnson [113, 115], who introduced nonsingular rings, in 1951, and …

Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

Throughout this paper R denotes an associative ring with unity. Recall from [Ka2) that R is a
Baer ring if the right annihilator of every nonempty subset of R is generated, as a right ideal …

For a ring R, we investigate and determine “minimal” right essential overrings (right ring
hulls) belonging to certain classes which are generated by R and subsets of the central …

We define a ring R to be right c P-Baer if the right annihilator of a cyclic projective right R-
module in R is generated by an idempotent. This class of rings generalizes the class of right …

We show the existence of principally (and finitely generated) right FI-extending right ring
hulls for semiprime rings. From this result, we prove that right principally quasi-Baer (ie, right …

Let V be a module with S= End (V). V is called a quasi-Baer module if for each ideal J of S, r
V (J)= e V for some e 2= e∈ S. On the other hand, V is called a Rickart module if for each …

Every module has an injective hull, a quasi-injective hull, and a quasi-continuous hull.
However, there exists a uniform nonsingular cyclic module over a noncommutative ring …

The notion of a Baer ring, introduced by Kaplansky, has been extended to that of a Baer
module using the endomorphism ring of a module in recent years. There do exist some …

We denote the maximal ring of quotients of R by Q (R) and the ring generated by the set of
all idempotents of Q (R) over R by C (R). In case jR is semiprime, C (R) coincides with the …