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τ-Injective Modules

  • Stelios Charalambides
  • John Clark
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this article we consider injective modules relative to a torsion theory τ. We introduce τ-M-injective and s-τ-M-injective modules, relatively τ-injective modules, the τ-M-injective hull and Σ-τ-M-injective and Σ-s-τ-M-injective modules. We then examine the relationship between these new and known concepts.

Some of the new results obtained include a Generalized Fuchs Criterion characterizing s-τ-M-injective modules, a Generalized Azumaya’s Lemma characterizing τ-⊕ I -M i -injective modules, the proof of the existence and uniqueness up to isomorphism of the τ-M-injective hull and generalizations of results by Albu and Năstăsescu, Faith, and Cailleau on necessary and sufficient conditions for a module to be Σ-s-τ-M-injective, Σ-τ-injective and for a direct sum of Σ-s-τ-M-injective modules to be Σ-s-τ-M-injective.

Keywords

Direct Summand Left Ideal Canonical Projection Injective Module Countable Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Stelios Charalambides
    • 1
  • John Clark
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand

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