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 …

1. Introduction. G. BERGMAN [1] investigated commutative pp rings and centers of left pp
rings (rings in which every left principal ideal is projective as a left module over the ring). W …

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 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 …

1. Introduction. In this paper a ring will mean a commutative ring with unity. An overring isa
subring of the total quotient ring which contains the given ring. A ring R is a P-ring if every …

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 …

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 …

In [1], S. Endo proved that if Л is a normal left pp ring, then for any ae A, there exist a central
indempotent e and a left. regular element d such that a= de. We prove that, in fact, normal pp …

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 …

On the structure of principal ideal rings Page 1 Pacific Journal of Mathematics ON THE
STRUCTURE OF PRINCIPAL IDEAL RINGS THOMAS WILLIAM HUNGERFORD Vol. 25, No. 3 …