Conditions for the endomorphism ring of a (finitely generated) projective module to be left
(semi) hereditary have been studied in several papers ([2],[7],[8]). In [2] and [8] it is shown …

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 …

Publisher Summary This chapter describes the hereditarily and cohereditarily projective
modules. There is a similarity between the study of n-firs and that of right semihereditary …

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

RINGS OF QUOTIENTS OF ENDOMORPHISM RINGS JL Gomez Pardo* Departamento de
Algebra. Universidad de Murcia. 30001 Murcia. Spain. Page 1 RINGS OF QUOTIENTS OF …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

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 …

Let R be a ring and M a fixed R-module. An R-module Q is called M-injective if, given a
monomorphism C $ of an R-module N into M, every homomorphism: N-+ Q can be extended …

Publisher Summary This chapter describes the different aspects of quotient rings. Quotient
rings that are constructed by Gabriel's method are nothing but the double centralizers of …

A right module M is called semi-projective if for every epimorphism α from M to a submodule
N of M and a homomorphism β from M to N, there exists a homomorphism γ from M to M with …