Fields With Finitely Many Non-Commutative Division Algebras Over Them

2023/07/29 by Sen, Snehinh
#11R52. Secondary: 12F05 #12D15 #16K50 #FOS: Mathematics #Primary: 12E15 #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2307.15914

Abstract

We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear lattice of finite field extensions over them.

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