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abx
abx
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The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra isalgebras are the finite extensions of $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra is $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebras are the finite extensions of $K$. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

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Emil Jeřábek
Emil Jeřábek
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The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra is $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebraCentral simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra is $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra is $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.

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abx
abx
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The classification is trivial for a $\,C_1$-field $K$ (that is, such that any homogeneous polynomial in $K[x_1,\ldots ,x_n]$ of degree $<n$ has a nontrivial zero): the only such division algebra is $K$ itself. For the proof you just need the notion of reduced norm, which can be explained in a reasonably elementary way (see Central simple algebra).

$C_1$-fields include finite fields and extensions of transcendance degree 1 of an algebraically closed field (Tsen's theorem); again, the proof in each case is relatively elementary.