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Questions about the proof of equivalence of two definitions of normal extensions in Lang's Algebra

score 84 · Answer 1 · 2026-04-11 01:14:34

84

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Questions about the proof of equivalence of two definitions of normal extensions in Lang's Algebra

Published on 11 Apr 2026 - 1:14

score 140 · Answer 2 · 2026-04-14 06:04:16

140

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Splitting field and primitive element

Published on 14 Apr 2026 - 6:04

score 77 · Answer 3 · 2026-04-14 07:42:30

77

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Examples for when the quotient ring is necessarily / not necessarily an extension of the residue field.

Published on 14 Apr 2026 - 7:42

score 257 · Answer 4 · 2026-04-16 15:53:28

257

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Proof of Theorem 4.6 (Primitive Element Theorem) in Lang's Algebra

Published on 16 Apr 2026 - 15:53

score 55 · Answer 5 · 2026-04-15 11:20:13

55

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Find irreducible polynomial

Published on 15 Apr 2026 - 11:20

score 55 · Answer 6 · 2026-04-14 08:36:40

55

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$(3)$ is inert in $\mathbb{Q}[\sqrt{2}]$

Published on 14 Apr 2026 - 8:36

score 87 · Answer 7 · 2026-04-15 02:23:10

87

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If $[R:Q]$ is cardinality equal to $R$?

Published on 15 Apr 2026 - 2:23

score 27 · Answer 8 · 2026-04-14 13:40:59

27

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Uniqueness of an embedded body extension in an algebraic closure

Published on 14 Apr 2026 - 13:40

score 60 · Answer 9 · 2026-04-12 04:28:37

60

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Understanding proof that subgroups of Galois group induces a simple, separable, and normal extension

Published on 12 Apr 2026 - 4:28

score 97 · Answer 10 · 2026-04-15 16:34:23

97

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Irreducible polynomial over $\mathbb{Q}_2$ & $\mathbb{Q}_3$

Published on 15 Apr 2026 - 16:34

score 34 · Answer 11 · 2026-04-12 01:12:13

34

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Simple extension of a simple extension

Published on 12 Apr 2026 - 1:12

score 120 · Answer 12 · 2026-04-15 09:32:13

120

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Generalization of rationalization algorithm

Published on 15 Apr 2026 - 9:32

score 77 · Answer 13 · 2026-04-17 12:57:22

77

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Is $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5}):\mathbb{Q}$ a simple extension?

Published on 17 Apr 2026 - 12:57

score 33 · Answer 14 · 2026-04-14 12:52:51

33

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Does there exist a subfield $K\subsetneq \mathbb{C}$ such that $x$ is transcendental over $K$ for all $x\notin K$?

Published on 14 Apr 2026 - 12:52

score 37 · Answer 15 · 2026-04-13 12:39:55

37

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Simple extensions being well-defined.

Published on 13 Apr 2026 - 12:39

List Question

Questions about the proof of equivalence of two definitions of normal extensions in Lang's Algebra

Splitting field and primitive element

Examples for when the quotient ring is necessarily / not necessarily an extension of the residue field.

Proof of Theorem 4.6 (Primitive Element Theorem) in Lang's Algebra

Find irreducible polynomial

$(3)$ is inert in $\mathbb{Q}[\sqrt{2}]$

If $[R:Q]$ is cardinality equal to $R$?

Uniqueness of an embedded body extension in an algebraic closure

Understanding proof that subgroups of Galois group induces a simple, separable, and normal extension

Irreducible polynomial over $\mathbb{Q}_2$ & $\mathbb{Q}_3$

Simple extension of a simple extension

Generalization of rationalization algorithm

Is $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5}):\mathbb{Q}$ a simple extension?

Does there exist a subfield $K\subsetneq \mathbb{C}$ such that $x$ is transcendental over $K$ for all $x\notin K$?

Simple extensions being well-defined.

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