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15
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Why is $\mathbb{Q}[\sqrt{-1}\,]$ special amongst $\mathbb{Q}[\sqrt{k}\,]$?

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#field-theory #galois-theory #extension-field
600
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Separable field extension of degree 2

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#abstract-algebra #field-theory #extension-field
296
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Inverse of polynomial over $\mathbb F_3$ finite field, quotient space

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#polynomials #finite-fields #extension-field
678
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galois norm and trace of field extensions

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#number-theory #galois-theory #extension-field
90
Views

$ \mathcal O_K/(p) \cong \mathbb F_p[T]/(T^n)$?

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#number-theory #algebraic-number-theory #p-adic-number-theory #extension-field
178
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On algebraically closed field

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#field-theory #galois-theory #extension-field
1.5k
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In characteristic $p$, the field extension $k(X,Y)$ over $k(X^p,Y^p)$ has degree $p^2$

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#abstract-algebra #field-theory #extension-field #positive-characteristic
1.1k
Views

In characteristic $p$, the field extension $k(X,Y)$ over $k(X^p,Y^p)$ is not simple

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#abstract-algebra #field-theory #extension-field #positive-characteristic
84
Views

Understanding a.. weird definition

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#abstract-algebra #definition #intuition #extension-field #roots-of-unity
88
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Irreducible polynomial in relatively algebraically closed extension

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#extension-field #irreducible-polynomials #transcendence-theory
106
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Algebraic Extension help!

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#field-theory #extension-field
4.3k
Views

find a splitting field of $x^4+x^2-1$ over $\mathbb{Q}$

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#galois-theory #extension-field
2.2k
Views

$F$ field, $\alpha$ separable on $F$. Is $F(\alpha)$ a separable extension of $F$?

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#polynomials #galois-theory #extension-field
4k
Views

Is Complex Numbers the biggest field? If yes, is there any easy proof to understand it?

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#abstract-algebra #complex-numbers #field-theory #extension-field
120
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field extension and equivalent automorphisms

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#galois-theory #extension-field

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