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Exercise 20 on Number Fields (Marcus) - Chapter 3

score 660 · Answer 1 · 2026-03-26 21:25:30

660

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Exercise 20 on Number Fields (Marcus) - Chapter 3

Published on 26 Mar 2026 - 21:25

score 1.8k · Answer 2 · 2026-02-23 08:21:47

1.8k

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Every simple ring is a division ring and vice versa.

Published on 23 Feb 2026 - 8:21

score 66 · Answer 3 · 2017-11-12 20:30:46

66

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A non-zero element in a prime ideal has a prime factor

Published on 12 Nov 2017 - 20:30

score 342 · Answer 4 · 2017-11-14 07:35:14

342

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When is a ring extension satisfying Going-Up and incomparability property , an integral extension?

Published on 14 Nov 2017 - 7:35

score 142 · Answer 5 · 2026-04-02 10:15:01

142

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For a localization of a ring $S^{-1}R,$ the extension of a prime ideal $P^e$ has no units if $P \cap S = \emptyset.$

Published on 02 Apr 2026 - 10:15

score 168 · Answer 6 · 2026-03-29 08:13:41

168

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Module projective

Published on 29 Mar 2026 - 8:13

score 380 · Answer 7 · 2017-11-19 00:22:33

380

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Exercise 5.6 of Cox's Primes of the Form $x^2 + ny^2$

Published on 19 Nov 2017 - 0:22

score 1.2k · Answer 8 · 2017-11-19 21:21:59

1.2k

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Maximal Ideals of Ring of real valued continuous functions defined over [0,1]

Published on 19 Nov 2017 - 21:21

score 841 · Answer 9 · 2026-03-28 11:53:41

841

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A surjective ring homomorphism can map a local ring to a local ring

Published on 28 Mar 2026 - 11:53

score 70 · Answer 10 · 2017-11-26 09:40:57

70

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Prove $J=\langle Y^{3}-X,Z^{5}-Y^{4}\rangle$ prime or $\mathbb{C}[X,Y,Z]/J$ integral domain.

Published on 26 Nov 2017 - 9:40

score 313 · Answer 11 · 2017-11-28 05:44:41

313

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Maximal ideals for the commutative ring formed by all infinite sequences of rational numbers that are constant after a point

Published on 28 Nov 2017 - 5:44

score 559 · Answer 12 · 2017-11-28 20:46:28

559

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If the intersections of ideals equal to a prime ideal, then at least one of the ideal equals to the prime ideal

Published on 28 Nov 2017 - 20:46

score 63 · Answer 13 · 2017-12-03 14:24:21

63

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Determine the maximal ideals of $R=\mathbb{Z}[\sqrt[4]{2},\sqrt[4]{2}\,i]$ containing 5.

Published on 03 Dec 2017 - 14:24

score 1.1k · Answer 14 · 2026-03-30 03:56:33

1.1k

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Prove that a UFD $R$ is a PID if every nonzero prime ideal in $R$ is maximal.

Published on 30 Mar 2026 - 3:56

score 972 · Answer 15 · 2026-03-29 03:10:53

972

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A ring is Noetherian if its prime ideals are ﬁnitely generated

Published on 29 Mar 2026 - 3:10

List Question

Exercise 20 on Number Fields (Marcus) - Chapter 3

Every simple ring is a division ring and vice versa.

A non-zero element in a prime ideal has a prime factor

When is a ring extension satisfying Going-Up and incomparability property , an integral extension?

For a localization of a ring $S^{-1}R,$ the extension of a prime ideal $P^e$ has no units if $P \cap S = \emptyset.$

Module projective

Exercise 5.6 of Cox's Primes of the Form $x^2 + ny^2$

Maximal Ideals of Ring of real valued continuous functions defined over [0,1]

A surjective ring homomorphism can map a local ring to a local ring

Prove $J=\langle Y^{3}-X,Z^{5}-Y^{4}\rangle$ prime or $\mathbb{C}[X,Y,Z]/J$ integral domain.

Maximal ideals for the commutative ring formed by all infinite sequences of rational numbers that are constant after a point

If the intersections of ideals equal to a prime ideal, then at least one of the ideal equals to the prime ideal

Determine the maximal ideals of $R=\mathbb{Z}[\sqrt[4]{2},\sqrt[4]{2}\,i]$ containing 5.

Prove that a UFD $R$ is a PID if every nonzero prime ideal in $R$ is maximal.

A ring is Noetherian if its prime ideals are ﬁnitely generated

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