Strictly invariant submodules

Simion Breaz; Grigore Călugăreanu; Andrey Chekhlov

Strictly invariant submodules

Rings and Algebras 2019-02-05 v1

Authors: Simion Breaz , Grigore Călugăreanu , Andrey Chekhlov

Abstract

If $M$ is an $R$ -module, we study the submodules $K\leq M$ with the property that $K$ is invariant with respect to all monomorphisms $K\rightarrow M$ . Such submodules are called \textsl{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 \textsl{strongly invariant}.

Keywords

module theory invariant theory abelian groups

Cite

@article{arxiv.1902.00940,
  title  = {Strictly invariant submodules},
  author = {Simion Breaz and Grigore Călugăreanu and Andrey Chekhlov},
  journal= {arXiv preprint arXiv:1902.00940},
  year   = {2019}
}

Comments

preprint version; the final version will be published by Mediterranean J. of Math

Strictly invariant submodules

Abstract

Keywords

Cite

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