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On $R$-Coneat Injective Modules and Generalizations

Mohanad Farhan Hamid

Abstract

Both the classes of $R$-coneat injective modules and its superclass, pure Baer injective modules, are shown to be preenveloping. The former class is contained in another one, namely, self coneat injectives, i.e. modules $M$ for which every map $f$ from a coneat left ideal of $R$ into $M$, whose kernel contains the annihilator of some element in $M$, is induced by a homomorphism $R \rightarrow M$. Certain types of rings are characterized by properties of the above modules. For instance, a commutative ring $R$ is von Neuman regular if and only if all self coneat injective $R$-modules are quasi injective.

On $R$-Coneat Injective Modules and Generalizations

Abstract

Both the classes of -coneat injective modules and its superclass, pure Baer injective modules, are shown to be preenveloping. The former class is contained in another one, namely, self coneat injectives, i.e. modules for which every map from a coneat left ideal of into , whose kernel contains the annihilator of some element in , is induced by a homomorphism . Certain types of rings are characterized by properties of the above modules. For instance, a commutative ring is von Neuman regular if and only if all self coneat injective -modules are quasi injective.
Paper Structure (3 sections, 13 theorems, 1 equation)

This paper contains 3 sections, 13 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. $R$-Coneat Injective Preenvelopes
  3. Self Coneat Injectivity

Key Result

Lemma \oldthetheorem

Every module has an $R$-coneat injective preenvelope.

Theorems & Definitions (21)

  • Lemma \oldthetheorem
  • proof
  • Lemma \oldthetheorem
  • Theorem \oldthetheorem
  • Corollary \oldthetheorem
  • Definition \oldthetheorem
  • Theorem \oldthetheorem
  • proof
  • Theorem \oldthetheorem
  • proof
  • ...and 11 more