ScholarLens Back to search
1991•Quaestiones MathematicaeRequires access

COPURE INJECTIVE MODULES

Edgar E. Enochs, Overtoun M. G. Jenda

Open publisher page 27 citations

Abstract

A module is said to be copure injective if it is injective with respect to all modules A ⊂ B with B/A injective. We first characterize submodules that have the extension property with respect to copure injective modules. Then we characterize commutative rings with finite self injective dimension in terms of copure injective modules. Finally, we show that the quotient categories of reduced copure injective modules and reduced h- divisible modules are isomorphic.

About this research paper

What this paper is about

A module is said to be copure injective if it is injective with respect to all modules A ⊂ B with B/A injective. We first characterize submodules that have the extension property with respect to copure injective modules. Then we characterize commutative rings with finite self injective dimension in terms of copure injective modules. Finally, we show that the quotient categories of reduced copure injective modules and reduced h- divisible modules are isomorphic.

Why it matters

OpenAlex reports 27 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A module is said to be copure injective if it is injective with respect to all modules A ⊂ B with B/A injective. We first characterize submodules that have the extension property with respect to copure injective modules. Then we characterize commutative rings with finite self injective dimension in terms of copure injective modules. Finally, we show that the quotient categories of reduced copure injective modules and reduced h- divisible modules are isomorphic.

Key concepts: Injective function, Injective module, Mathematics, Monomorphism, Divisible group, Module, Horizontal line test, Pure mathematics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
COPURE INJECTIVE MODULES — Research Paper | ScholarLens