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Why does the cardinality of the vector space over a finite field of characteristic $p$ have to be a power of $p$?

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#linear-algebra #vector-spaces #finite-fields #positive-characteristic
525
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$x\mapsto x^p$ with $\operatorname{char}(F)=p>0$ is a ring homomorphism

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#ring-homomorphism #positive-characteristic
51
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A homomorphism on a nontrivial commutative ring with trivial unit group

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#abstract-algebra #ring-theory #commutative-algebra #ring-homomorphism #positive-characteristic
196
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Transforming Quadrics in Characteristic 2

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#algebraic-geometry #projective-geometry #quadratic-forms #positive-characteristic #quadrics
221
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Are simple Lie algebras complete?

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#lie-algebras #positive-characteristic
283
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Finite Characteristic of a Ring

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#abstract-algebra #ring-theory #positive-characteristic
71
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A question on regular local rings (of positive characteristic ) of dimension $2$

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#algebraic-geometry #commutative-algebra #positive-characteristic #regular-rings
1k
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The group algebra is not semisimple if characteristic divides group order.

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#abstract-algebra #modules #representation-theory #positive-characteristic
202
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Frobenius twist of a field

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#linear-algebra #algebraic-geometry #vector-spaces #commutative-algebra #positive-characteristic
78
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Character group of diagonalizable group has no $p$-torsion

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#algebraic-groups #characters #positive-characteristic
97
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Algebraic de Rham cohomology of the affine plane in characteristic p?

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#reference-request #differential-forms #affine-varieties #de-rham-cohomology #positive-characteristic
341
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Do invariants and co-invariants for a cyclic group have the same dimension?

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#representation-theory #positive-characteristic
328
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A corollary of Schur's lemma in positive characteristic

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#linear-algebra #representation-theory #positive-characteristic
215
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Semisimple representation theory of finite groups in characteristic p.

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#finite-groups #representation-theory #positive-characteristic
84
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Prime factors of a separable polynomial in a non-splitting field.

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#abstract-algebra #field-theory #positive-characteristic #separable-extension

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