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arXiv · 2010.15486

Endomorphism rings via minimal morphisms

Manuel Cortés-Izurdiaga·Pedro A. Guil Asensio·D. Keskin Tütüncü·Ashish K. Srivastava
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Abstract

We prove that if $u:K \rightarrow M$ is a left minimal extension, then there exists an isomorphism between two subrings, $\textrm{End}_R^M(K)$ and $\textrm{End}_R^K(M)$ of $\textrm{End}_R(K)$ and $\textrm{End}_R(M)$ respectively, modulo their Jacobson radicals. This isomorphism is used to deduce properties of the endomorphism ring of $K$ from those of the endomorphism ring of $M$ in certain situations such us when $K$ is invariant under endomorphisms of $M,$ or when $K$ is invariant under automorphisms of $M$.

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Manuel Cortés-Izurdiaga, Pedro A. Guil Asensio, D. Keskin Tütüncü, Ashish K. Srivastava. 2020-10-29. Endomorphism rings via minimal morphisms. https://arxiv.org/abs/2010.15486

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