List questions from positive-characteristic

Published on 10 Sep 2017 - 3:09

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Can a finite ring have a characteristic $0$?

Published on 13 Nov 2017 - 15:45

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Multiple roots for roots of unity in fields of some characteristic

Published on 23 Dec 2017 - 14:12

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Weil pairing on $E[p]$ is trivial

Published on 30 Dec 2017 - 10:37

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The local ring $(R,\mathfrak{m})$ contains a field if and only if $\mathrm{char}(R) = \mathrm{char} (R/\mathfrak{m})$.

Published on 22 Mar 2026 - 4:44

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Example of infinite field of characteristic $p\neq 0$

Published on 22 Mar 2026 - 0:48

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How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?

Published on 22 Mar 2026 - 12:07

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Problem in Jacobson's Basic Algebra (Vol. I)

Published on 22 Mar 2026 - 5:35

95

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Rank of $R^n$ in characteristic $n$

Published on 31 Jul 2020 - 17:01

140

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Morphisms between K3 surfaces

Published on 25 Mar 2026 - 9:12

34

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Showing that a polynomial splits in a splitting field of another polynomial

Published on 10 Aug 2020 - 19:30

180

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The quotient of the Weyl algebra by its centre is a matrix algebra

Published on 11 Aug 2020 - 14:33

191

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How to understand this statement: A finite field with $n$ elements exists iff $n=p^k$, where $p$ is a prime and $k$ a positive integer

Published on 13 Aug 2020 - 6:54

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Conjugates in Field Theory

Published on 24 Aug 2020 - 9:06

311

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Prove that $m$ divides the characteristic of $R.$

Published on 14 Sep 2020 - 14:41

List Question

Middle Terms do not cancel correctly when calculating the Discriminant of the Frey Curve

Can a finite ring have a characteristic $0$?

Multiple roots for roots of unity in fields of some characteristic

Weil pairing on $E[p]$ is trivial

The local ring $(R,\mathfrak{m})$ contains a field if and only if $\mathrm{char}(R) = \mathrm{char} (R/\mathfrak{m})$.

Example of infinite field of characteristic $p\neq 0$

How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?

Problem in Jacobson's Basic Algebra (Vol. I)

Rank of $R^n$ in characteristic $n$

Morphisms between K3 surfaces

Showing that a polynomial splits in a splitting field of another polynomial

The quotient of the Weyl algebra by its centre is a matrix algebra

How to understand this statement: A finite field with $n$ elements exists iff $n=p^k$, where $p$ is a prime and $k$ a positive integer

Conjugates in Field Theory

Prove that $m$ divides the characteristic of $R.$

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