… The main aim of the present paper is generalizing von Neumann regular rings, PP rings,
and Baer rings to a general module theoretic setting respectively from another point of view. …

… Recall that a ring is right Rickart (also called right pp-ring) if the right annihilator of each …
(GC) The ring R satisfies the generalized comparability if for every two projections p and q, there …

… rings are studied and some characterizations of von Neumann regular rings and PP rings …
A π-regular ring is called (von Neumann) regular when n = 1. According to Huh et al. [14], a …

… (Citation2003, Theorem 2.3), we know that a ring R is von Neumann regular if and only if R
is a right AP-injective and right PP ring. We … Clearly, every Baer ring is a right and left PP ring. …

… pp condition [2, Theorem 3.4] and without the pp condition [2, Theorem 2.2]. The former result
is generalized in [5] to reduced pp rings. … The following condit reduced Baer ring ; (b) Every …

… Note that reduced pp rings generalize effectively strongly regular rings. … von Neumann
regular iff every left (right) J.-module is p-injective. It is well-known that A is von Neumann regular …

… the aforementioned generalizations of complemented rings (… of the von Neumann regular
property such as weak Baer (ie, … complemented, weak Baer (pp), and feebly Baer (almost pp), …

… pp rings and Baer rings in relation to their quotient rings. First, … The next is a slight
generalization of [1, Lemma 3.1], [3, … quotient ring C of the center of R is a von Neumann regular …

… PP rings (hence all hereditary semiprimary rings), all right (left) nonsingular right (left) CS
rings, and all von Neumann regular rings … generalized to the concept of a piecewise prime ring (…

… Rickart showed that all von Neumann algebras satisfy the … In 1950 Kaplansky figured out
that von Neumann algebras, in fact, … The class of generalized pp \( \ast \)-rings (which are also …