Question

let $R$ be a Ring, show that p is a prime element if and only if (p) is a prime ideal in $R$.

score 340 · Answer 1 · 2021-01-04 15:49:29

340

Views

let $R$ be a Ring, show that p is a prime element if and only if (p) is a prime ideal in $R$.

Published on 04 Jan 2021 - 15:49

score 58 · Answer 2 · 2021-01-04 21:17:25

58

Views

Is the ideal $I := (7X+14, X^3+2X^2+1) \subseteq \mathbb Z[X]$ prime? Is it maximal?

Published on 04 Jan 2021 - 21:17

score 206 · Answer 3 · 2021-01-05 05:11:20

206

Views

Let $P$ and $Q$ be prime ideals of a ring $R$ such that every element of $R\setminus (P\cup Q)$ is a unit. Prove that either $P$ or $Q$ is maximal.

Published on 05 Jan 2021 - 5:11

score 76 · Answer 4 · 2021-01-11 05:55:02

76

Views

$A\neq \{0\}$ is a unit commutative ring. If $a\in A-\{0\}$ is such that for all $b\in A$, $a\ast b=0$ or $a\ast b=a$. Then $(1+a)$ is prime ideal

Published on 11 Jan 2021 - 5:55

score 436 · Answer 5 · 2021-01-11 10:55:38

436

Views

Inverse image of a non-zero prime ideal under a surjective ring homomorphism

Published on 11 Jan 2021 - 10:55

score 136 · Answer 6 · 2026-03-27 23:48:37

136

Views

Finding zero divisors of quotient rings $\mathbb{C}[x,y,z]/I$

Published on 27 Mar 2026 - 23:48

score 213 · Answer 7 · 2026-03-25 13:54:04

213

Views

Unique maximal ideal and ring epimorphism kernel with prime numbers equivalence

Published on 25 Mar 2026 - 13:54

score 57 · Answer 8 · 2021-01-15 21:16:21

57

Views

$m \subset R$ is maximal $\iff$ $0 \subset R / m$ is maximal

Published on 15 Jan 2021 - 21:16

score 145 · Answer 9 · 2021-01-16 11:39:38

145

Views

maximal ideal of $K[x,y]$ is generated by two elements

Published on 16 Jan 2021 - 11:39

score 124 · Answer 10 · 2021-01-17 21:18:02

124

Views

How to find all the maximal ideals that contain $(X+2Z+1,Y-Z,Z^2+Z+1)$ in $\mathbb{C}[X,Y,Z]$

Published on 17 Jan 2021 - 21:18

score 49 · Answer 11 · 2021-01-17 22:09:39

49

Views

How to calculate all the maximal ideals that contain $(X-1,Y-1,T^6+Z^6+Z^5,Z+X)$ in $\mathbb{K}[X,Y,Z,T]$

Published on 17 Jan 2021 - 22:09

score 290 · Answer 12 · 2026-03-25 12:54:53

290

Views

every ideal in a Noetherian ring is an intersection of ideals primary to maximal ideals?

Published on 25 Mar 2026 - 12:54

score 1.3k · Answer 13 · 2021-01-18 09:22:23

1.3k

Views

Find all prime ideals and maximal ideals of $\mathbb{Z}_{36}$

Published on 18 Jan 2021 - 9:22

score 237 · Answer 14 · 2026-03-26 19:05:10

237

Views

How we can know the ramification ideals geometrically?

Published on 26 Mar 2026 - 19:05

score 77 · Answer 15 · 2021-01-22 19:53:24

77

Views

Determine if an ideal is prime in $\mathbb{Z}[\sqrt{-5}]$

Published on 22 Jan 2021 - 19:53

List Question

let $R$ be a Ring, show that p is a prime element if and only if (p) is a prime ideal in $R$.

Is the ideal $I := (7X+14, X^3+2X^2+1) \subseteq \mathbb Z[X]$ prime? Is it maximal?

Let $P$ and $Q$ be prime ideals of a ring $R$ such that every element of $R\setminus (P\cup Q)$ is a unit. Prove that either $P$ or $Q$ is maximal.

$A\neq \{0\}$ is a unit commutative ring. If $a\in A-\{0\}$ is such that for all $b\in A$, $a\ast b=0$ or $a\ast b=a$. Then $(1+a)$ is prime ideal

Inverse image of a non-zero prime ideal under a surjective ring homomorphism

Finding zero divisors of quotient rings $\mathbb{C}[x,y,z]/I$

Unique maximal ideal and ring epimorphism kernel with prime numbers equivalence

$m \subset R$ is maximal $\iff$ $0 \subset R / m$ is maximal

maximal ideal of $K[x,y]$ is generated by two elements

How to find all the maximal ideals that contain $(X+2Z+1,Y-Z,Z^2+Z+1)$ in $\mathbb{C}[X,Y,Z]$

How to calculate all the maximal ideals that contain $(X-1,Y-1,T^6+Z^6+Z^5,Z+X)$ in $\mathbb{K}[X,Y,Z,T]$

every ideal in a Noetherian ring is an intersection of ideals primary to maximal ideals?

Find all prime ideals and maximal ideals of $\mathbb{Z}_{36}$

How we can know the ramification ideals geometrically?

Determine if an ideal is prime in $\mathbb{Z}[\sqrt{-5}]$

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