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Rings all of whose torsion quasi-injective modules are injective

Published online by Cambridge University Press:  18 May 2009

J. Ahsan  and
E. Enochs
J. Ahsan
Affiliation:
Department of Mathematics, University Of Kentucky, Lexington, Kentucky 40506, U.S.A.
E. Enochs
Affiliation:
Department of Mathematics, University Of Kentucky, Lexington, Kentucky 40506, U.S.A.
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Throughout this paper it is assumed that rings are associative, have the identity element, and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R-modules, and for each left R-module M, E(M) (resp. J(M)) will represent the injective hull (resp. Jacobson radical) of M. Also, for a module M, A ⊆' M will mean that A is an essential submodule of M, and Z(M) denotes the singular submodule of M. M is called singular if Z(M) = M, and it is called non-singular in case Z(M) = 0. For fundamental definitions and results related to torsion theories, we refer to [12] and [14]. In this paper we shall deal mainly with Goldie torsion theory. Recall that a pair (G, F) of classes of left R-modules is known as Goldie torsion theory if G is the smallest torsion class containing all modules B/A, where A ⊆' B, and the torsion free class F is precisely the class of non-singular modules.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 219 - 227
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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