Geodesic
Commutative nearly absolute valued algebras with square roots
Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 207-216.

Voir la notice de l'article provenant de la source International Press of Boston

Let $A$ be a commutative nearly absolute valued algebra. In this note we prove that all elements of $A$ have square roots if and only if $A$ is a two-dimensional real division algebra. This can be viewed as a generalization of a well-known theorem of Hopf.
DOI : 10.4310/HHA.2018.v20.n2.a10
Classification : 17A35, 46H70, 55N10
Keywords: division algebra, singular homology group, commutative algebra, square root, fundamental group 
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     title = {Commutative nearly absolute valued algebras with square roots},
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     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a10/}
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José Antonio Cuenca Mira; Francisca Miguel García. Commutative nearly absolute valued algebras with square roots. Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 207-216. doi : 10.4310/HHA.2018.v20.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a10/

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