In this paper we study non-commutative pp rings and Baer rings in relation to their quotient
rings. First, we investigate right pp rings and their classical quotient rings. It has been shown …

Introduction. In [3], GM Bergman gave characterizations of semihe-reditary and hereditary
commutative rings in terms of their Pierce stalks. In preparation for these, he also gave …

A ring R is called a left PP-ring if every principal left ideal is projective, equivalently if the left
annihilator l (a) is generated by an idempotent for all a∈ R. These rings seem first to have …

This paper consists of two parts. In the first part, it is proven that a ring R is right PP if and
only if every right R-module has a monic PI-cover, where PI denotes the class of all P …

In this note we present some results on divisible pp rings. A ring with identity is called (right)
principal projective (pp) iff every prin cipal (right) ideal is projective. In [3] a divisible ring is …

The purpose of this paper is to study further the ideal and module structure of a commutative
ring with identity, in which every principal ideal is projective. Results concerning particular …

Throughout the paper, rings are associative rings with identity. A ring is called right duo if
every right ideal is two-sided, and it is called right pp if every principal right ideal is …

A ring R is called a right PCI-ring if and only if for any cyclic right R-module C either C≅ R or
C is injective. Faith has shown that right PCI-rings are either semiprime Artinian or simple …

This paper is a supplement to the author [2]. Let Λ be a ring with identity. If every principal left
ideal in Λ is Λ-projective, then Hattori and Nakano called Λ a left PP-ring in [3],[4]. Nakano …

This paper concerns two conditions, called right pp and generalized right pp, which are
generalizations of Baer rings and von Neumann regular rings. We study the subrings and …