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15
122
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Question about Lang's Chapter 6 Theorem 9.1

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#abstract-algebra #polynomials #field-theory #galois-theory #irreducible-polynomials
116
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Splitting Fields over arbitrary fields

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#field-theory #extension-field #splitting-field
311
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Doubt in Lang's proof that normal extensions remain normal under lifting (Theorem V.3.4, *Algebra*)

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#abstract-algebra #field-theory #extension-field #normal-extension
75
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Number of possible extensions of field into algebraically closed field

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#field-theory
38
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How do you go about calculating this degree $[F_{p^2}(t)(t^{1/p}):F_p(t)]$

Published on
#field-theory #galois-theory
108
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Trace map for extension of local fields

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#abstract-algebra #field-theory #valuation-theory
37
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Separable polynomial in field and its extension

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#field-theory
169
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Proof of separability of polynomials without derivatives

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#abstract-algebra #polynomials #field-theory #alternative-proof #separable-extension
375
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Tower of fields and quadratic extensions

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#abstract-algebra #field-theory #extension-field
200
Views

Definition and some theorems on separable extensions

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#field-theory
48
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Prove $\Bbb{Q}(M)=\Bbb{Q}(N)$ where $M=\{ \sqrt{r} | r \in \Bbb{Q}\} \subseteq \Bbb{C},N=\{ \sqrt{1-a^2} | a \in \mathbb{Q}\} \subseteq \Bbb{C}$

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#field-theory #extension-field
149
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Proving the surjective property in Chinese Remainder Theorem

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#ring-theory #field-theory #chinese-remainder-theorem
1.4k
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Ideal generated by two elements is maximal in $\mathbb{Z}[x]$

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#abstract-algebra #ring-theory #field-theory #ideals #maximal-and-prime-ideals
36
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Prove that $p(x) = \alpha (x)f(x) + \beta (x)g(x)$ for some irreducible $f(x)$, $g(x)$.

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#field-theory #irreducible-polynomials
112
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How many countable non-isomorphic models does $\text{ACF}_p$ have?

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#abstract-algebra #field-theory #model-theory

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