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Strictly Invariant Submodules

  • Simion Breaz
  • Grigore CălugăreanuEmail author
  • Andrey Chekhlov
Article
  • 47 Downloads

Abstract

If M is an R-module, we study the submodules \(K\le M\) with the property that K is invariant with respect to all monomorphisms \(K\rightarrow M\). Such submodules are called strictly invariant. For the case of \( \mathbb {Z}\)-modules (i.e. Abelian groups), we prove that in many situations these submodules are invariant with respect to all homomorphisms \( K\rightarrow M\), submodules which were called strongly invariant.

Keywords

Strictly invariant submodule strongly invariant submodule Abelian group strictly invariant subgroup 

Mathematics Subject Classification

16D10 16D80 20K27 

Notes

Acknowledgements

Thanks are due to the referee, for corrections and suggestions which improved our presentation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Faculty of Mechanics and MathematicsTomsk State UniversityTomskRussia

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