Question

Theoretical justification of method to find the minimal polynomial of $\alpha=\sqrt p + \sqrt q$ over $\mathbb Q$ with $p,q $ distinct prime numbers

score 102 · Answer 1 · 2026-04-16 11:58:57

102

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Theoretical justification of method to find the minimal polynomial of $\alpha=\sqrt p + \sqrt q$ over $\mathbb Q$ with $p,q $ distinct prime numbers

Published on 16 Apr 2026 - 11:58

score 122 · Answer 2 · 2026-04-11 14:47:48

122

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Are all fields the field of fractions of an integral domain that is not a field?

Published on 11 Apr 2026 - 14:47

score 74 · Answer 3 · 2026-04-15 18:29:50

74

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$\mathbf{Z}(M_n(F))\cong F$ for all fields $F$

Published on 15 Apr 2026 - 18:29

score 44 · Answer 4 · 2026-04-09 02:28:46

44

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Understanding the uniqueness of the ring of fraction proof in D&F.

Published on 09 Apr 2026 - 2:28

score 97 · Answer 5 · 2026-04-12 02:46:52

97

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what is the difference between Theorem 15 and Problem 7.5.2 in Dummit & Foote

Published on 12 Apr 2026 - 2:46

score 56 · Answer 6 · 2026-04-17 09:46:42

56

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Do we have $[H_1H_2:H_1]=[H_2:H_1\cap H_2]$?

Published on 17 Apr 2026 - 9:46

score 102 · Answer 7 · 2026-04-14 19:57:35

102

Views

Dummit and Foote 13.2.9

Published on 14 Apr 2026 - 19:57

score 58 · Answer 8 · 2026-04-13 20:49:46

58

Views

A group closed under scalar multiplication is a vector space

Published on 13 Apr 2026 - 20:49

score 174 · Answer 9 · 2026-04-09 04:11:19

174

Views

Prove that $\mathcal{O}$ is a Euclidean Domain.

Published on 09 Apr 2026 - 4:11

score 182 · Answer 10 · 2026-04-15 10:32:13

182

Views

Let $L$ be the splitting field of the polynomial $ f$ over $K$, Prove that if $n!=[L:K]$, the polynomial is irreducible

Published on 15 Apr 2026 - 10:32

score 103 · Answer 11 · 2026-04-15 08:31:12

103

Views

Splitting field and degree of extension of $x^4 + 2x^2 -2$ over $\mathbb F_{13}$

Published on 15 Apr 2026 - 8:31

score 57 · Answer 12 · 2026-05-10 23:30:42

57

Views

Sub algebras of dimension $2$ of division algebras

Published on 10 May 2026 - 23:30

score 61 · Answer 13 · 2026-04-15 13:26:09

61

Views

Orders and invertible ideals of a quadratic number field

Published on 15 Apr 2026 - 13:26

score 42 · Answer 14 · 2026-04-17 09:11:14

42

Views

Under which circumstances can the class number of a quadratic form not degenerate into the class number of imaginary quadratic fields?

Published on 17 Apr 2026 - 9:11

score 128 · Answer 15 · 2026-04-15 05:29:57

128

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Is $x^6 + bx^3 + b^2$ irreducible?

Published on 15 Apr 2026 - 5:29

List Question

Theoretical justification of method to find the minimal polynomial of $\alpha=\sqrt p + \sqrt q$ over $\mathbb Q$ with $p,q $ distinct prime numbers

Are all fields the field of fractions of an integral domain that is not a field?

$\mathbf{Z}(M_n(F))\cong F$ for all fields $F$

Understanding the uniqueness of the ring of fraction proof in D&F.

what is the difference between Theorem 15 and Problem 7.5.2 in Dummit & Foote

Do we have $[H_1H_2:H_1]=[H_2:H_1\cap H_2]$?

Dummit and Foote 13.2.9

A group closed under scalar multiplication is a vector space

Prove that $\mathcal{O}$ is a Euclidean Domain.

Let $L$ be the splitting field of the polynomial $ f$ over $K$, Prove that if $n!=[L:K]$, the polynomial is irreducible

Splitting field and degree of extension of $x^4 + 2x^2 -2$ over $\mathbb F_{13}$

Sub algebras of dimension $2$ of division algebras

Orders and invertible ideals of a quadratic number field

Under which circumstances can the class number of a quadratic form not degenerate into the class number of imaginary quadratic fields?

Is $x^6 + bx^3 + b^2$ irreducible?

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