List questions from cyclotomic-fields

Published on 26 Feb 2020 - 5:07

164

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Why in cyclotomic extension, Gal($K/F$) may not isomorphic to the whole $Z/nZ$?

Published on 02 Mar 2020 - 15:23

48

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Proof of a relation of Stickelberger element

Published on 06 Mar 2020 - 10:05

102

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subfields of the cyclotomic fields $\mathbb{Q}(\zeta_p)$ with $p \equiv 1 [5]$

Published on 08 Mar 2020 - 21:07

140

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Fermat's Little Theorem in cyclotomic fields

Published on 10 Mar 2020 - 6:31

53

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Congruence in cyclotomic fields

Published on 11 Mar 2020 - 22:31

77

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The action of a Galois group on a cyclotomic field.

Published on 15 Mar 2020 - 13:03

250

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Factoring Primes in cyclotomic fields

Published on 31 Mar 2020 - 18:14

90

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Group of Units a Subgroup of some ${S}_n$

Published on 01 Apr 2020 - 16:42

105

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Algebraic Integers of a Field

Published on 07 Apr 2020 - 21:03

181

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On the irreducibility over cyclotomic field in radical extension.

Published on 08 Apr 2020 - 5:41

68

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Proving that $\mathbb{Z}[e^{2i\pi/23}]$ is not a PID

Published on 08 Apr 2020 - 13:38

67

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Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

Published on 08 Apr 2020 - 22:41

120

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Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Published on 09 Apr 2020 - 5:20

66

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Prove that $(1 - \omega)^{\phi(m)} = p$ where $\omega = e^{2\pi i/m}$

Published on 14 Apr 2020 - 16:20

List Question

Proof of a relation of elements in group rings

Why in cyclotomic extension, Gal($K/F$) may not isomorphic to the whole $Z/nZ$?

Proof of a relation of Stickelberger element

subfields of the cyclotomic fields $\mathbb{Q}(\zeta_p)$ with $p \equiv 1 [5]$

Fermat's Little Theorem in cyclotomic fields

Congruence in cyclotomic fields

The action of a Galois group on a cyclotomic field.

Factoring Primes in cyclotomic fields

Group of Units a Subgroup of some ${S}_n$

Algebraic Integers of a Field

On the irreducibility over cyclotomic field in radical extension.

Proving that $\mathbb{Z}[e^{2i\pi/23}]$ is not a PID

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Prove that $(1 - \omega)^{\phi(m)} = p$ where $\omega = e^{2\pi i/m}$

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