2013/02/03 by Pedro A. Guil Asensio, Asensio, Pedro A. Guil, Ashish K. Srivastava +1
Materials Science · Mathematics · #16D50 #16U60 #16W20 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Synthesis and properties of polymers #math.RA #msc:16D50 #msc:16U60 #msc:16W20
paper · pdf · doi:10.48550/arxiv.1302.0443
To appear in Contemporary Mathematics Series of American Math. Society
arxiv created 2013/02/03 · openalex publication_date 2013/02/03 · arxiv updated 2013/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.