Question

The dimension of a division ring over its center is square.

score 505 · Answer 1 · 2026-03-20 01:39:50

505

Views

The dimension of a division ring over its center is square.

Published on 20 Mar 2026 - 1:39

score 414 · Answer 2 · 2026-03-20 06:35:36

414

Views

Prove that the homomorphism $\phi:R\to S^{-1}R$ is injective if and only if $S$ contains no zero-divisors.

Published on 20 Mar 2026 - 6:35

score 42 · Answer 3 · 2026-03-21 22:59:32

42

Views

Why does the multiplication in a division algebra depends on every component?

Published on 21 Mar 2026 - 22:59

score 120 · Answer 4 · 2026-03-22 13:15:51

120

Views

Degree $n$ extension of local field splits degree $n$ division algebra

Published on 22 Mar 2026 - 13:15

score 375 · Answer 5 · 2026-03-20 06:53:37

375

Views

Galois theory for (non-commutative) division rings

Published on 20 Mar 2026 - 6:53

score 133 · Answer 6 · 2026-03-22 16:12:04

133

Views

Conditions for equivalent definitions of division algebra

Published on 22 Mar 2026 - 16:12

score 112 · Answer 7 · 2026-03-20 03:04:12

112

Views

Existence of division algebras with center $\mathbb{Q}$ of prime degree

Published on 20 Mar 2026 - 3:04

score 389 · Answer 8 · 2026-03-19 22:24:01

389

Views

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Published on 19 Mar 2026 - 22:24

score 61 · Answer 9 · 2026-03-22 16:27:45

61

Views

How to construction a division ring from the given field?

Published on 22 Mar 2026 - 16:27

score 158 · Answer 10 · 2026-03-20 17:27:45

158

Views

The ring generated over the center of a division ring by a group.

Published on 20 Mar 2026 - 17:27

score 87 · Answer 11 · 2026-03-20 07:08:27

87

Views

Central simple quaternion algebra: why is the matrix for $\rho(v)$ antidiagonal?

Published on 20 Mar 2026 - 7:08

score 230 · Answer 12 · 2026-03-25 03:01:06

230

Views

Central simple algebras give rise to algebraic groups

Published on 25 Mar 2026 - 3:01

score 219 · Answer 13 · 2026-03-20 08:01:24

219

Views

Brauer group of the field of Laurent series with coefficients in a finite field

Published on 20 Mar 2026 - 8:01

score 89 · Answer 14 · 2026-03-20 23:16:00

89

Views

Classification of a certain family of real division algebras

Published on 20 Mar 2026 - 23:16

score 98 · Answer 15 · 2026-03-22 06:40:32

98

Views

Subfields of central division algebras over fixed global field

Published on 22 Mar 2026 - 6:40

List Question

The dimension of a division ring over its center is square.

Prove that the homomorphism $\phi:R\to S^{-1}R$ is injective if and only if $S$ contains no zero-divisors.

Why does the multiplication in a division algebra depends on every component?

Degree $n$ extension of local field splits degree $n$ division algebra

Galois theory for (non-commutative) division rings

Conditions for equivalent definitions of division algebra

Existence of division algebras with center $\mathbb{Q}$ of prime degree

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

How to construction a division ring from the given field?

The ring generated over the center of a division ring by a group.

Central simple quaternion algebra: why is the matrix for $\rho(v)$ antidiagonal?

Central simple algebras give rise to algebraic groups

Brauer group of the field of Laurent series with coefficients in a finite field

Classification of a certain family of real division algebras

Subfields of central division algebras over fixed global field

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