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arXiv · 1302.0443

Additive Unit Representations in Endomorphism Rings and an Extension of a result of Dickson and Fuller

Pedro A. Guil Asensio·Ashish K. Srivastava
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Abstract

A module is called automorphism-invariant if it is invariant under any automorphism of its injective hull. Dickson and Fuller have shown that if $R$ is a finite-dimensional algebra over a field $\mathbb F$ with more than two elements then an indecomposable automorphism-invariant right $R$-module must be quasi-injective. In this note, we extend and simplify the proof of this result by showing that any automorphism-invariant module over an algebra over a field with more than two elements is quasi-injective. Our proof is based on the study of the additive unit structure of endomorphism rings.

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Pedro A. Guil Asensio, Ashish K. Srivastava. 2013-02-03. Additive Unit Representations in Endomorphism Rings and an Extension of a result of Dickson and Fuller. https://arxiv.org/abs/1302.0443

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