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arXiv · 1902.00940

Strictly invariant submodules

Simion Breaz·Grigore Călugăreanu·Andrey Chekhlov
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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}.

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Simion Breaz, Grigore Călugăreanu, Andrey Chekhlov. 2019-02-03. Strictly invariant submodules. https://arxiv.org/abs/1902.00940

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