List questions from splitting-field

Published on 30 Mar 2026 - 2:11

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Proving a polynomial splits fully in a certain field

Published on 03 Dec 2020 - 17:29

119

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In the real quaternion ring, for any $t$ where $t^2=-1$, there exists a $s$ such that $sts^{-1} = i$

Published on 04 Dec 2020 - 4:10

75

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Is any algebraic extension a subfield of a spitting field?

Published on 20 Dec 2020 - 7:49

95

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Calculating the degree of a splitting field of $f(x)=x^4-4x^3-4x^2+16x-8$ over $\mathbb{Q}$.

Published on 27 Dec 2020 - 19:01

41

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Field extension of $\mathbb{Q}$ is the splitting field of two different polynomials?

Published on 25 Mar 2026 - 19:04

295

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Degree of $\mathbb{Q}(2^{\frac{1}{3}},\omega)$ over $\mathbb{Q}(2^{\frac{1}{3}})$

Published on 28 Dec 2020 - 19:42

235

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Splitting field of $8$-th root of the unity is Galois

Published on 28 Mar 2026 - 4:35

322

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Splitting field of a polynomial over $\mathbb{Z_3}$

Published on 08 Jan 2021 - 16:07

386

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Factorization of Polynomial in an extension field

Published on 09 Jan 2021 - 10:04

107

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Subfields of splitting field

Published on 10 Jan 2021 - 23:33

75

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confused about Lemma 5.28 in Rotman's A First Course in Abstract Algebra

Published on 16 Jan 2021 - 3:57

195

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Galois group of an irreducible polynomial of degree 4 is not cyclic

Published on 30 Mar 2026 - 3:56

52

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Splitting field and intersection of subfields

Published on 24 Jan 2021 - 21:09

27

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zeros in simple algebraic extenison

Published on 25 Jan 2021 - 12:25

List Question

Non cyclic Galois extension of degree 12

Proving a polynomial splits fully in a certain field

In the real quaternion ring, for any $t$ where $t^2=-1$, there exists a $s$ such that $sts^{-1} = i$

Is any algebraic extension a subfield of a spitting field?

Calculating the degree of a splitting field of $f(x)=x^4-4x^3-4x^2+16x-8$ over $\mathbb{Q}$.

Field extension of $\mathbb{Q}$ is the splitting field of two different polynomials?

Degree of $\mathbb{Q}(2^{\frac{1}{3}},\omega)$ over $\mathbb{Q}(2^{\frac{1}{3}})$

Splitting field of $8$-th root of the unity is Galois

Splitting field of a polynomial over $\mathbb{Z_3}$

Factorization of Polynomial in an extension field

Subfields of splitting field

confused about Lemma 5.28 in Rotman's A First Course in Abstract Algebra

Galois group of an irreducible polynomial of degree 4 is not cyclic

Splitting field and intersection of subfields

zeros in simple algebraic extenison

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