Question

What is this problem asking for? "Prove that the residue of $A$ in $R/P$ has rank $1$ for every prime ideal $P$ of $R$"

score 117 · Answer 1 · 2026-03-25 23:13:07

117

Views

What is this problem asking for? "Prove that the residue of $A$ in $R/P$ has rank $1$ for every prime ideal $P$ of $R$"

Published on 25 Mar 2026 - 23:13

score 511 · Answer 2 · 2018-04-17 03:42:58

511

Views

Axioms of a Ring and a Simple Example (that confused me)

Published on 17 Apr 2018 - 3:42

score 417 · Answer 3 · 2026-03-26 07:59:30

417

Views

"Let $R$ be an integral domain. Assuming that the Division Algorithm holds in $R[x]$, prove that $R$ is a field."

Published on 26 Mar 2026 - 7:59

score 599 · Answer 4 · 2018-04-17 15:35:27

599

Views

How to define the '*' operation in the ring

Published on 17 Apr 2018 - 15:35

score 46 · Answer 5 · 2026-03-25 01:21:43

46

Views

Largest ring over which a particular abelian group becomes a module

Published on 25 Mar 2026 - 1:21

score 86 · Answer 6 · 2018-04-17 18:30:29

86

Views

Given epimorphism $\phi$ and ideal $I$, with $\operatorname{Ker}\phi \subseteq I$, prove $\phi(\sqrt{I}) = \sqrt{\phi(I)}$

Published on 17 Apr 2018 - 18:30

score 923 · Answer 7 · 2026-03-25 01:22:25

923

Views

All homomorphisms from $\mathbb{Q}$ to $\mathbb{Q}$ are isomorphisms

Published on 25 Mar 2026 - 1:22

score 667 · Answer 8 · 2026-03-20 05:24:36

667

Views

Ring of Gaussian integers modulo p=4n+3

Published on 20 Mar 2026 - 5:24

score 34 · Answer 9 · 2018-04-17 19:33:18

34

Views

Ring with a set of vectors

Published on 17 Apr 2018 - 19:33

score 394 · Answer 10 · 2018-04-17 22:51:14

394

Views

Subrings and ideals of subring $\mathbb{Q}_p$ of $\mathbb{Q}$

Published on 17 Apr 2018 - 22:51

score 111 · Answer 11 · 2026-03-22 19:58:19

111

Views

Basis for the vector space over $\mathbb{Q}$

Published on 22 Mar 2026 - 19:58

score 400 · Answer 12 · 2026-03-25 18:49:11

400

Views

Is $\langle x^2+1,y\rangle$ maximal or prime in $\Bbb{R}[x,y]$ or $\Bbb{C}[x,y]$

Published on 25 Mar 2026 - 18:49

score 269 · Answer 13 · 2018-04-18 11:37:32

269

Views

Number elements in $\Bbb{Z}[i]/\langle3+i\rangle$

Published on 18 Apr 2018 - 11:37

score 44 · Answer 14 · 2026-03-25 23:10:41

44

Views

Prime ideals in ring and polynomial rings

Published on 25 Mar 2026 - 23:10

score 2.2k · Answer 15 · 2026-03-25 18:49:04

2.2k

Views

Finding all the maximal ideals of $C([0,1])$ and also prime ideals in it which are not maximal

Published on 25 Mar 2026 - 18:49

List Question

What is this problem asking for? "Prove that the residue of $A$ in $R/P$ has rank $1$ for every prime ideal $P$ of $R$"

Axioms of a Ring and a Simple Example (that confused me)

"Let $R$ be an integral domain. Assuming that the Division Algorithm holds in $R[x]$, prove that $R$ is a field."

How to define the '*' operation in the ring

Largest ring over which a particular abelian group becomes a module

Given epimorphism $\phi$ and ideal $I$, with $\operatorname{Ker}\phi \subseteq I$, prove $\phi(\sqrt{I}) = \sqrt{\phi(I)}$

All homomorphisms from $\mathbb{Q}$ to $\mathbb{Q}$ are isomorphisms

Ring of Gaussian integers modulo p=4n+3

Ring with a set of vectors

Subrings and ideals of subring $\mathbb{Q}_p$ of $\mathbb{Q}$

Basis for the vector space over $\mathbb{Q}$

Is $\langle x^2+1,y\rangle$ maximal or prime in $\Bbb{R}[x,y]$ or $\Bbb{C}[x,y]$

Number elements in $\Bbb{Z}[i]/\langle3+i\rangle$

Prime ideals in ring and polynomial rings

Finding all the maximal ideals of $C([0,1])$ and also prime ideals in it which are not maximal

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