List questions from ring-theory

Published on 15 Mar 2018 - 4:45

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Maximal ideals in Artinian ring

Published on 15 Mar 2018 - 8:35

155

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Determine if this is a field

Published on 15 Mar 2018 - 10:05

243

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$R \cong R[[x]]$

Published on 15 Mar 2018 - 14:14

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What does the notation of “1=/= 0” mean for “Let R be a ring with unity 1=/= 0”?

Published on 15 Mar 2018 - 14:26

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Are the rings $\mathbb{Q}[X]/(X^3-1)$ and $\mathbb{Q}[X]/(X^3+1)$ isomorphic?

Published on 15 Mar 2018 - 18:17

46

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Does a map with these properties have a name?

Published on 15 Mar 2018 - 18:39

591

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Isomorphism of inverse limits.

Published on 25 Mar 2026 - 0:06

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Prove that two polynomials $f,g \in k[X]$ have a common root in $\bar k$ iff $f,g$ have a common factor in $k[X])$.

Published on 26 Mar 2026 - 18:51

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Elements and structure of units in $\mathbb Q(\sqrt {-7})$

Published on 16 Mar 2018 - 19:59

174

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Example of primary ideal whose radical is not finitely generated

Published on 17 Mar 2018 - 5:37

852

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Is there an example of a power of prime ideal in a polynomial ring that is not primary?

Published on 25 Mar 2026 - 17:20

151

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Polynomial ring as a finite algebra over a subring

Published on 25 Mar 2026 - 17:19

149

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Tower of integral extensions

Published on 22 Mar 2026 - 0:19

2.9k

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Prime in $\mathbb Z [\sqrt{-5}]$ but not in $\mathbb Z [\sqrt{5}]$

Published on 17 Mar 2018 - 12:12

List Question

$p(x)x^n+q(x)(1-x)^n=1$ for some $p(x), q(x)\in \mathbb{Z}[x]$, what explicitly $p(x), q(x)$ are?

Maximal ideals in Artinian ring

Determine if this is a field

$R \cong R[[x]]$

What does the notation of “1=/= 0” mean for “Let R be a ring with unity 1=/= 0”?

Are the rings $\mathbb{Q}[X]/(X^3-1)$ and $\mathbb{Q}[X]/(X^3+1)$ isomorphic?

Does a map with these properties have a name?

Isomorphism of inverse limits.

Prove that two polynomials $f,g \in k[X]$ have a common root in $\bar k$ iff $f,g$ have a common factor in $k[X])$.

Elements and structure of units in $\mathbb Q(\sqrt {-7})$

Example of primary ideal whose radical is not finitely generated

Is there an example of a power of prime ideal in a polynomial ring that is not primary?

Polynomial ring as a finite algebra over a subring

Tower of integral extensions

Prime in $\mathbb Z [\sqrt{-5}]$ but not in $\mathbb Z [\sqrt{5}]$

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