Question

Ideals of $\mathbb{Z}[\zeta_{p}]$ factorise uniquely

score 116 · Answer 1 · 2017-04-01 13:04:51

116

Views

Ideals of $\mathbb{Z}[\zeta_{p}]$ factorise uniquely

Published on 01 Apr 2017 - 13:04

score 62 · Answer 2 · 2017-04-01 14:55:10

62

Views

does this hold for roots of zero dimensional ideals?

Published on 01 Apr 2017 - 14:55

score 62 · Answer 3 · 2017-04-02 07:12:45

62

Views

Find a ring with exactly 2009 ideals

Published on 02 Apr 2017 - 7:12

score 63 · Answer 4 · 2017-04-02 10:43:47

63

Views

Let $R=\mathbb{Z}[i]=\{a+bi\mid a,b\in\mathbb{Z}\}$, where $i^2 =−1$, and let $I=(3+i)$. Find the exact number of elements in $R/I$.

Published on 02 Apr 2017 - 10:43

score 1.6k · Answer 5 · 2026-03-26 08:15:07

1.6k

Views

An ideal which is nil but not nilpotent

Published on 26 Mar 2026 - 8:15

score 63 · Answer 6 · 2026-04-01 03:45:46

63

Views

$f(x)$ such that $f (0)$ is not $0$ but $f(1) = 0$. So $(f(x) + I)$ is an element. But how would this element have an inverse

Published on 01 Apr 2026 - 3:45

score 245 · Answer 7 · 2026-03-26 19:18:31

245

Views

Are maximal Ideals in $\mathbb{Z}[\sqrt 2]$ equal when their quotient rings are isomorphic?

Published on 26 Mar 2026 - 19:18

score 69 · Answer 8 · 2017-04-04 01:44:37

69

Views

Intuitively, I know that $x$ is not in the ideal generated by $x^2, y^2$. How do I prove this rigorously?

Published on 04 Apr 2017 - 1:44

score 46 · Answer 9 · 2017-04-04 20:48:14

46

Views

Ideals Containing Ideals

Published on 04 Apr 2017 - 20:48

score 203 · Answer 10 · 2017-04-05 03:38:33

203

Views

If we take $R$ to be the field of real numbers. Show that $R[x]/\langle x^2 + 1\rangle$ is a field.

Published on 05 Apr 2017 - 3:38

score 196 · Answer 11 · 2017-04-05 04:32:33

196

Views

Show every prime ideal in $\mathbb{Z}$ is of form $\langle p\rangle$ where $p$ is prime.

Published on 05 Apr 2017 - 4:32

score 129 · Answer 12 · 2017-04-06 08:29:40

129

Views

Is there an integral domain $R$ with ideal $I$ such that $I^2 = I$ and $I$ is nontrivial?

Published on 06 Apr 2017 - 8:29

score 79 · Answer 13 · 2026-03-26 07:39:16

79

Views

Proprieties of Kernel of Subring of Field

Published on 26 Mar 2026 - 7:39

score 106 · Answer 14 · 2017-04-07 21:38:23

106

Views

Is $(1+\sqrt{-5})$ an ideal of $\mathbb{Z}[\sqrt{-5}]$?

Published on 07 Apr 2017 - 21:38

score 77 · Answer 15 · 2017-04-08 23:57:53

77

Views

Simplifying $R=\mathbb{Z}[x]/I$

Published on 08 Apr 2017 - 23:57

List Question

Ideals of $\mathbb{Z}[\zeta_{p}]$ factorise uniquely

does this hold for roots of zero dimensional ideals?

Find a ring with exactly 2009 ideals

Let $R=\mathbb{Z}[i]=\{a+bi\mid a,b\in\mathbb{Z}\}$, where $i^2 =−1$, and let $I=(3+i)$. Find the exact number of elements in $R/I$.

An ideal which is nil but not nilpotent

$f(x)$ such that $f (0)$ is not $0$ but $f(1) = 0$. So $(f(x) + I)$ is an element. But how would this element have an inverse

Are maximal Ideals in $\mathbb{Z}[\sqrt 2]$ equal when their quotient rings are isomorphic?

Intuitively, I know that $x$ is not in the ideal generated by $x^2, y^2$. How do I prove this rigorously?

Ideals Containing Ideals

If we take $R$ to be the field of real numbers. Show that $R[x]/\langle x^2 + 1\rangle$ is a field.

Show every prime ideal in $\mathbb{Z}$ is of form $\langle p\rangle$ where $p$ is prime.

Is there an integral domain $R$ with ideal $I$ such that $I^2 = I$ and $I$ is nontrivial?

Proprieties of Kernel of Subring of Field

Is $(1+\sqrt{-5})$ an ideal of $\mathbb{Z}[\sqrt{-5}]$?

Simplifying $R=\mathbb{Z}[x]/I$

Trending Questions

Popular # Hahtags

Popular Questions