List questions from ideals

Published on 29 Mar 2026 - 2:46

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$\beta\alpha$ in ideal $I$ for all $\alpha\in I$ $\implies$ $\beta$ is algebraic integer

Published on 10 Sep 2016 - 9:32

800

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Maximal ideals over non-field polynomial ring

Published on 31 Mar 2026 - 12:20

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In what other ways can this chain of ideals ascend?

Published on 10 Sep 2016 - 21:35

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Unique minimal prime over an ideal

Published on 26 Mar 2026 - 16:06

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$(f) = (c)(g)$, where $R$ is a UFD, $c \in R$, $f,g \in R[x]$, and $g$ is primitive

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258

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If every element in a prime ideal $I$ is nilpotent, then $I=\sqrt{0}$?

Published on 12 Sep 2016 - 13:06

64

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Working with Principal Ideal Domains

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How do maximal homogeneous ideals look like in polynomial ring?

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Self-injectivity of quotients of polynomial rings by zero-dimensional ideals

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48

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If two elements are not $\mathcal R$-equivalent in some semigroup, then their homomorphic images are also not $\mathcal R$-equivalent

Published on 26 Mar 2026 - 13:00

167

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Is there a ring without unity which can be expressed as a union of its three proper ideals?

Published on 25 Mar 2026 - 12:53

137

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Proof that $A[[X_1,\ldots,X_r]]$ is complete in the $(X_1,\ldots,X_r)$-adic topology.

Published on 17 Sep 2016 - 18:05

324

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Gröbner bases over $\mathbb{Z}[x]$

Published on 25 Mar 2026 - 13:53

240

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The prime ideals of the ring $\mathbb{C} \otimes \mathbb{C}$

Published on 18 Sep 2016 - 14:14

List Question

Maximal ideals of $B[y]$ where $B$ is PID.

$\beta\alpha$ in ideal $I$ for all $\alpha\in I$ $\implies$ $\beta$ is algebraic integer

Maximal ideals over non-field polynomial ring

In what other ways can this chain of ideals ascend?

Unique minimal prime over an ideal

$(f) = (c)(g)$, where $R$ is a UFD, $c \in R$, $f,g \in R[x]$, and $g$ is primitive

If every element in a prime ideal $I$ is nilpotent, then $I=\sqrt{0}$?

Working with Principal Ideal Domains

How do maximal homogeneous ideals look like in polynomial ring?

Self-injectivity of quotients of polynomial rings by zero-dimensional ideals

If two elements are not $\mathcal R$-equivalent in some semigroup, then their homomorphic images are also not $\mathcal R$-equivalent

Is there a ring without unity which can be expressed as a union of its three proper ideals?

Proof that $A[[X_1,\ldots,X_r]]$ is complete in the $(X_1,\ldots,X_r)$-adic topology.

Gröbner bases over $\mathbb{Z}[x]$

The prime ideals of the ring $\mathbb{C} \otimes \mathbb{C}$

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