Question

Two elements $x,y$ not nilpotent implies $\exists a$ in ring and $n, m > 0$ such that $a^n=x$, $a^m=y$?

score 127 · Answer 1 · 2017-03-18 23:05:50

127

Views

Two elements $x,y$ not nilpotent implies $\exists a$ in ring and $n, m > 0$ such that $a^n=x$, $a^m=y$?

Published on 18 Mar 2017 - 23:05

score 908 · Answer 2 · 2026-04-01 00:31:04

908

Views

How to factor in cubic extensions?

Published on 01 Apr 2026 - 0:31

score 976 · Answer 3 · 2017-03-19 23:47:41

976

Views

Show that the set of prime ideals of A has minimal element with respect to inclusion

Published on 19 Mar 2017 - 23:47

score 82 · Answer 4 · 2017-03-20 06:24:01

82

Views

Any polynomial ring contains a prime element?

Published on 20 Mar 2017 - 6:24

score 367 · Answer 5 · 2017-03-20 06:52:05

367

Views

For a ring $R$ with a single proper ideal $I$, show that $I$ is prime

Published on 20 Mar 2017 - 6:52

score 117 · Answer 6 · 2026-03-25 22:04:51

117

Views

Product of Ideals in Ring that is not UFD

Published on 25 Mar 2026 - 22:04

score 269 · Answer 7 · 2017-03-24 09:13:08

269

Views

Are the Following Two Equivalent Characterizations of Co-prime Ideals?

Published on 24 Mar 2017 - 9:13

score 1.5k · Answer 8 · 2026-03-26 11:17:22

1.5k

Views

Nilpotent Radical is contained in the intersection of all prime ideals

Published on 26 Mar 2026 - 11:17

score 749 · Answer 9 · 2026-03-29 12:57:25

749

Views

$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element

Published on 29 Mar 2026 - 12:57

score 93 · Answer 10 · 2017-03-24 21:58:41

93

Views

How to prove that if a product is in a prime ideal, then one of the factors must be?

Published on 24 Mar 2017 - 21:58

score 109 · Answer 11 · 2017-03-25 14:23:57

109

Views

The prime ideals of $\mathbb{Z} [x] \otimes_{\mathbb{Z}} \mathbb{F}_p$

Published on 25 Mar 2017 - 14:23

score 187 · Answer 12 · 2017-03-28 20:02:46

187

Views

Why does a simple Lie algebra have zero radical?

Published on 28 Mar 2017 - 20:02

score 644 · Answer 13 · 2026-03-26 21:09:16

644

Views

find all ideals of quotient ring $Q[x]/I$

Published on 26 Mar 2026 - 21:09

score 62 · Answer 14 · 2017-04-02 16:41:28

62

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 02 Apr 2017 - 16:41

score 245 · Answer 15 · 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

List Question

Two elements $x,y$ not nilpotent implies $\exists a$ in ring and $n, m > 0$ such that $a^n=x$, $a^m=y$?

How to factor in cubic extensions?

Show that the set of prime ideals of A has minimal element with respect to inclusion

Any polynomial ring contains a prime element?

For a ring $R$ with a single proper ideal $I$, show that $I$ is prime

Product of Ideals in Ring that is not UFD

Are the Following Two Equivalent Characterizations of Co-prime Ideals?

Nilpotent Radical is contained in the intersection of all prime ideals

$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element

How to prove that if a product is in a prime ideal, then one of the factors must be?

The prime ideals of $\mathbb{Z} [x] \otimes_{\mathbb{Z}} \mathbb{F}_p$

Why does a simple Lie algebra have zero radical?

find all ideals of quotient ring $Q[x]/I$

$f(x)$ 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?

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