List questions from division-ring

Published on 10 Nov 2017 - 19:03

247

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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 25 Nov 2017 - 8:30

236

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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 29 Nov 2017 - 13:22

60

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Division in higher dimensional ring of formal power series

Published on 23 Feb 2026 - 2:57

147

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Find a way to represent $\mathbb{H}$ as a subring of $M_{4}(\mathbb{R}).$

Published on 28 Sep 2020 - 21:05

178

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Must an abstract $C^*$-algebra that is an integral domain be a field?

Published on 23 Feb 2026 - 4:59

71

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Show that $\mathbb{Z}[\sqrt{3}]$ satisfies the following division property:

Published on 05 Nov 2020 - 23:32

1k

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Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

Published on 15 Nov 2020 - 5:18

85

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Analogue of primitive element theorem for division rings

Published on 15 Nov 2020 - 9:58

1.1k

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A finite ring without zero divisors is a division ring

Published on 01 Dec 2020 - 17:18

120

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On the opposite group

Published on 20 Dec 2020 - 17:01

1.1k

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Show that a finite domain is a division ring

Published on 01 Feb 2021 - 18:21

1k

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Division Ring and Integral Domain

Published on 08 Mar 2021 - 9:33

137

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Let V be an infinite dimensional vector space over a division ring D. The Set F={θ:V→V: Im(θ) is a finite dimensional subspace of V} is a simple ring.

Published on 22 Mar 2021 - 17:15

154

Views

What is minimal polynomial over a skew field?

Published on 23 Mar 2021 - 10:22

List Question

Every simple ring is a division ring and vice versa.

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 $D$?

Division in higher dimensional ring of formal power series

Find a way to represent $\mathbb{H}$ as a subring of $M_{4}(\mathbb{R}).$

Must an abstract $C^*$-algebra that is an integral domain be a field?

Show that $\mathbb{Z}[\sqrt{3}]$ satisfies the following division property:

Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

Analogue of primitive element theorem for division rings

A finite ring without zero divisors is a division ring

On the opposite group

Show that a finite domain is a division ring

Division Ring and Integral Domain

Let V be an infinite dimensional vector space over a division ring D. The Set F={θ:V→V: Im(θ) is a finite dimensional subspace of V} is a simple ring.

What is minimal polynomial over a skew field?

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