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Quasinjective Modules and Selfinjective Rings

  • Carl Faith
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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 191)

Abstract

If M is a module such that every map f: SM of a submodule S is induced by an endomorphism of M, then M is said to be quasinjective, or QI, for short. Every module which is injective modulo annihilator, and every semisimple module, is QI (see 19.2). The QI modules coincide with the class of fully invariant sub-modules of injective modules 19.3. A module which is finitely generated over endomorphism ring is said to be finendo. Any finendo QI module is injective modulo annihilator 19.14A. Over a right Artinian ring, any QI right module is finendo and conversely 19.16. Thus, every faithful quasinjective over a right Artinian ring is injective 19.15, a result which holds for finitely generated faithful modules over commutative rings 19.17.

Keywords

Prime Ideal Left Ideal Prime Ring Endomorphism Ring Regular Ring 
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

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Carl Faith
    • 1
    • 2
  1. 1.Rutgers, The State UniversityNew BrunswickUSA
  2. 2.The Institute for Advanced StudyPrincetonUSA

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