List questions from division-algebras

Published on 23 Feb 2026 - 4:51

52

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A proper subring of an 4-dimensional division F-algebra is a field.

Published on 23 Feb 2026 - 6:24

92

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Are division algebras over local fields compact mod center?

Published on 04 Jul 2017 - 1:17

344

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Dimension of division rings extension

Published on 10 Sep 2017 - 14:56

238

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Primitive element theorem for division rings extension

Published on 12 Sep 2017 - 18:47

70

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Multiplicativity formula for a tower of division algebras

Published on 23 Feb 2026 - 6:22

273

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The division ring of fractions of the first Weyl algebra and its subrings

Published on 23 Feb 2026 - 6:25

161

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finite division algebras over a field

Published on 17 Sep 2017 - 9:20

94

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Fields for $\mathbb Q^3$?

Published on 24 Sep 2017 - 21:32

230

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Let $D$ be a countably dimensional division algebra over an uncountable algebraically closed field $F$. Why $D=F$?

Published on 24 Nov 2017 - 8:01

248

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Let $D$ be a division ring. Show that if every $a \in D$ is algebraic over the prime subfield of $D$ then $D$ is commutative

Published on 23 Feb 2026 - 8:28

237

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If $R$ is a finitely generated $D$-algebra, $D$ a division ring, then $R$ has finite basis over $D$?

Published on 23 Feb 2026 - 8:25

273

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Dimension of $End(V)$ with $V$ countable dimension irreducible module over a complex algebra

Published on 22 Dec 2017 - 12:51

9.7k

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What are some real-world uses of Octonions?

Published on 25 Mar 2026 - 23:38

11.5k

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linear algebra over a division ring vs. over a field

Published on 13 Jun 2011 - 6:48

List Question

Indefinite unitary group over split quaternions

A proper subring of an 4-dimensional division F-algebra is a field.

Are division algebras over local fields compact mod center?

Dimension of division rings extension

Primitive element theorem for division rings extension

Multiplicativity formula for a tower of division algebras

The division ring of fractions of the first Weyl algebra and its subrings

finite division algebras over a field

Fields for $\mathbb Q^3$?

Let $D$ be a countably dimensional division algebra over an uncountable algebraically closed field $F$. Why $D=F$?

Let $D$ be a division ring. Show that if every $a \in D$ is algebraic over the prime subfield of $D$ then $D$ is commutative

If $R$ is a finitely generated $D$-algebra, $D$ a division ring, then $R$ has finite basis over $D$?

Dimension of $End(V)$ with $V$ countable dimension irreducible module over a complex algebra

What are some real-world uses of Octonions?

linear algebra over a division ring vs. over a field

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