OF A PROJECTIVE MODULE OVER A QUASI-HEREDITARY RING Page 1 PROCEEDINGS
OF the AMERICAN MATHEMATICAL SOCIETY Volume 107. Number I. September 1989 …

We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a
direct sum of countably generated modules [2, Theorem l]. If any direct summand A of a …

Introduction. A ring is called left (right) hereditary in case each left (right) ideal is projective.
Such rings have been studied extensively, and the property of being left hereditary is …

QUASI-INJECTIVE AND PSEUDO-INFECTIVE MODULES Page 1 Canad. Math. Bull. Vol. 18
(3), 1975 QUASI-INJECTIVE AND PSEUDO-INFECTIVE MODULES BY SK JAIN AND SURJEET …

Y. Utumi (14 and 15) obtained some interesting results on self-injective rings. He showed
that, if R is right self-injective, then so is R/J, where J is the Jacobson radical of R. Also, if R …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …

Hereditary rings Page 1 HEREDITARY RINGS AA Tuganbaev All rings are assumed to be
associative with a nonzero unity element. A distributive module is a module with a distributive …

Let R be a ring. A right R-module M is called quasi-principally(or semi-) injective if it is M-
principally inj ective. In this paper, we show:(1) The following are equivalent for a projective …

1. Introduction. A ring is (right) semihereditary if every finitelygenerated right ideal is
projective. Chase [2] gave the first example of a ring which was right but not left …

The object of this paper is to prove Theorem. For a ring $ R $ the following are equivalent:(i)
Every cyclic right $ R $-module is injective or projective.(ii) $ R= S\oplus T $ where $ S $ is …