Question

A prime ideal in a polynomial ring whose intersection with the base ring is zero

score 225 · Answer 1 · 2018-11-30 11:25:25

225

Views

A prime ideal in a polynomial ring whose intersection with the base ring is zero

Published on 30 Nov 2018 - 11:25

score 117 · Answer 2 · 2026-03-25 11:13:43

117

Views

An element lies in a prime ideal but not in its square

Published on 25 Mar 2026 - 11:13

score 949 · Answer 3 · 2018-12-02 13:33:23

949

Views

Basic properties of complete intersection ideals

Published on 02 Dec 2018 - 13:33

score 352 · Answer 4 · 2026-03-28 13:40:13

352

Views

Prove that $R$ has exactly one nontrivial ideal

Published on 28 Mar 2026 - 13:40

score 236 · Answer 5 · 2026-03-28 13:40:20

236

Views

Question about transitivity of ideals

Published on 28 Mar 2026 - 13:40

score 166 · Answer 6 · 2018-12-03 19:51:00

166

Views

Principal ideal is equal to a unit multiplied by the principal ideal

Published on 03 Dec 2018 - 19:51

score 228 · Answer 7 · 2018-12-04 22:00:01

228

Views

Is this correct? $N(\langle a, b \rangle) = \gcd(N(a), N(b))$

Published on 04 Dec 2018 - 22:00

score 168 · Answer 8 · 2018-12-05 21:32:43

168

Views

Ideal of distinct points

Published on 05 Dec 2018 - 21:32

score 36 · Answer 9 · 2026-02-23 07:01:04

36

Views

If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

Published on 23 Feb 2026 - 7:01

score 79 · Answer 10 · 2026-03-25 07:46:26

79

Views

$\bigcap_{n\in\mathbb{N}} I^n = (0)$ if and only if no zero divisor of $R$ is of the form $1-z$ with $z\in I$.

Published on 25 Mar 2026 - 7:46

score 77 · Answer 11 · 2026-03-28 13:42:21

77

Views

If $J$ is an ideal of $R$ that is maximal in the set of ideals of $R$ that annihilate elements of $R/I$, then $J$ is a prime ideal of $R$.

Published on 28 Mar 2026 - 13:42

score 127 · Answer 12 · 2026-03-25 09:29:13

127

Views

Prove $(0) = (x)\cap (xz^{n-1} + \lambda y^n)$ in $R=\frac{k[x,y,z]}{(x^2,xy)}$

Published on 25 Mar 2026 - 9:29

score 539 · Answer 13 · 2018-12-08 19:08:20

539

Views

Why is the radical ideal of the homogenization of an ideal the homogenization of the radical of said ideal?

Published on 08 Dec 2018 - 19:08

score 570 · Answer 14 · 2018-12-08 23:44:57

570

Views

Ideals generated by two elements in $\mathbb{Z}[x]$

Published on 08 Dec 2018 - 23:44

score 1.2k · Answer 15 · 2018-12-10 23:37:34

1.2k

Views

Let R be a commutative ring, and I, J denote two ideals in R such that I + J = R. Is it true that IJ = I ∩ J?

Published on 10 Dec 2018 - 23:37

List Question

A prime ideal in a polynomial ring whose intersection with the base ring is zero

An element lies in a prime ideal but not in its square

Basic properties of complete intersection ideals

Prove that $R$ has exactly one nontrivial ideal

Question about transitivity of ideals

Principal ideal is equal to a unit multiplied by the principal ideal

Is this correct? $N(\langle a, b \rangle) = \gcd(N(a), N(b))$

Ideal of distinct points

If $g = gcd(a,b)$ prove (a,b)=(g). Furthermore, if $k = lcm(a,b)$ prove that $(a)\cap(b) = (k)$

$\bigcap_{n\in\mathbb{N}} I^n = (0)$ if and only if no zero divisor of $R$ is of the form $1-z$ with $z\in I$.

If $J$ is an ideal of $R$ that is maximal in the set of ideals of $R$ that annihilate elements of $R/I$, then $J$ is a prime ideal of $R$.

Prove $(0) = (x)\cap (xz^{n-1} + \lambda y^n)$ in $R=\frac{k[x,y,z]}{(x^2,xy)}$

Why is the radical ideal of the homogenization of an ideal the homogenization of the radical of said ideal?

Ideals generated by two elements in $\mathbb{Z}[x]$

Let R be a commutative ring, and I, J denote two ideals in R such that I + J = R. Is it true that IJ = I ∩ J?

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