List questions from ideals

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Find example of nonhomogeneous ideal in $\mathbb{k}[x]$ which has two different minimal generating sets are not equipotent.

Published on 04 Oct 2018 - 15:08

78

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Diophantine Equations over polynomial rings

Published on 27 Mar 2026 - 2:50

53

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Radicals and Ideals

Published on 06 Oct 2018 - 9:54

72

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Examples for ideals that can not be finitely generated

Published on 26 Mar 2026 - 18:58

1.2k

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Sum of ideals equals R implies the sum of their powers is R

Published on 08 Oct 2018 - 17:32

687

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Is contraction of radical ideals and/or prime ideals surjective in this case?

Published on 10 Oct 2018 - 3:46

189

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radical of the Jacobian ideal

Published on 12 Oct 2018 - 17:37

161

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On projective ideals

Published on 26 Mar 2026 - 23:09

188

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Ideal $I$ in a Noetherian ring such that $I+(b)$ and $I+(a)$ are projective, where $ab\in I$

Published on 26 Mar 2026 - 21:27

792

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Can you always define the sum of ideals?

Published on 13 Oct 2018 - 1:29

36

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On a special type of ideal in local Artinian ring

Published on 25 Mar 2026 - 3:02

302

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Ideals of $\Bbb{Z}_4[X]/(X^2+X+1)$

Published on 28 Mar 2026 - 10:04

466

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Show that every maximal ideal of $R$ contains the element $a$.

Published on 25 Mar 2026 - 11:33

31

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If $R$ is a ring such that $x^2=x$ $\forall x \in R$ and $I$ is a prime ideal. Show that $R/I$ has two elements

Published on 28 Mar 2026 - 11:44

71

Views

Every left ideal of $R[x]$ is cyclic implies $R$ a division ring

Published on 23 Mar 2026 - 10:55

List Question

Find example of nonhomogeneous ideal in $\mathbb{k}[x]$ which has two different minimal generating sets are not equipotent.

Diophantine Equations over polynomial rings

Radicals and Ideals

Examples for ideals that can not be finitely generated

Sum of ideals equals R implies the sum of their powers is R

Is contraction of radical ideals and/or prime ideals surjective in this case?

radical of the Jacobian ideal

On projective ideals

Ideal $I$ in a Noetherian ring such that $I+(b)$ and $I+(a)$ are projective, where $ab\in I$

Can you always define the sum of ideals?

On a special type of ideal in local Artinian ring

Ideals of $\Bbb{Z}_4[X]/(X^2+X+1)$

Show that every maximal ideal of $R$ contains the element $a$.

If $R$ is a ring such that $x^2=x$ $\forall x \in R$ and $I$ is a prime ideal. Show that $R/I$ has two elements

Every left ideal of $R[x]$ is cyclic implies $R$ a division ring

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