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15
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Is $\mathbb{F}_q(x)$ a perfect field?

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#field-theory #separable-extension
120
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Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?

Published on
#field-theory #separable-extension
129
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smallest normal extension containing an infinite algebraic extension

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#field-theory #normal-extension
174
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$\mathbb{R}$ with usual $+$, but not multiplication

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#field-theory #real-numbers
784
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Restriction of automorphism to a fixed field an automorphism of the fixed field?

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#abstract-algebra #field-theory #galois-theory
465
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Prove that if $f:R\rightarrow S$ is a semiring homomorphism and $R$ is a ring, then $S$ is a ring as well.

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#abstract-algebra #ring-theory #field-theory
1.8k
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Dimension of vector space generated by finite field over its subfield

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#linear-algebra #vector-spaces #field-theory #finite-fields
175
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Prove that an element of a quotient ring of polynomials is algebraic

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#abstract-algebra #polynomials #field-theory
985
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Finite dimensional associative division algebras over Q

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#abstract-algebra #ring-theory #vector-spaces #commutative-algebra #field-theory
122
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Preserving transcendence degree

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#abstract-algebra #polynomials #field-theory #extension-field #transcendence-theory
134
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A curious extension of real number field?

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#linear-algebra #abstract-algebra #ring-theory #field-theory #extension-field
1.1k
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basis for the splitting field of $x^3 - 3$ over the rationals

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#abstract-algebra #polynomials #field-theory #extension-field #splitting-field
47
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Subfield has at most $p^n$ elements.

Published on
#abstract-algebra #field-theory
175
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Set-theoretic equality of splitting fields within a fixed algebraic closure

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#abstract-algebra #elementary-set-theory #field-theory #splitting-field
632
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Can algebraic numbers be compared using only rational arithmetic?

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#abstract-algebra #field-theory #algorithms #ordered-fields

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