GENERALIZATIONS OF INJECTIVE MODULES

Abstract

Let R be a ring with identity. Given a positive integer n, a unitary right R-module X is called n–injective provided, for every n-generated right ideal A of R, every R-homomorphism φ : A → X can be lifted to R. In this note we investigate this and related injectivity conditions and show that there are many rings R which have an n–injective module which is not (n+1)– injective.

Keywords

• injective module, semihereditary ring

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12. Esperanza S´anchez Campos Departamento de ´Algebra Geometr´ıa y Topolog´ıa Universidad de M´alaga M´alaga, Spain e-mail: [e-mail] Patrick F. Smith Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland UK e-mail: [e-mail]