List questions from ideals

Published on 25 Mar 2026 - 14:03

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Let $R$ be a commutative ring. For $a \in R$ consider the set $(a) = \{r*a | r\in R\}$. Show that $(a) = R$ if a is a unit of $R$

Published on 15 Apr 2026 - 14:00

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Ideals of Unique Factorization Domain

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Build a reduced ring starting from an ordinary one

Published on 13 Apr 2026 - 0:26

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The ideal generated by $(x,y) \cdot (x,z) \cdot (y,z)$ in $k[x,y,z]$ for a field $k$

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Expressing a hypersurface of a variety as zero locus

Published on 14 Apr 2026 - 0:21

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How do I show $(f_1(x), f_2(x), ..., x-a) = (f_1(a), ..., f_r(a), x-a)$ where $a \in R$, $R$ is a commutative ring, $f_i(x) \in R[x]$

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Does localization commute with taking radicals?

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203

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$(x_1, ..., x_k)$ is prime in $R[x_1, ..., x_n]$ if $R$ is an integral domain

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503

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Generator of intersection of ideals in a PID via adjunction?

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Nilpotent or non-Nilpotent Jacobson Radical

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936

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For an algebraically closed field $k$, an ideal $I$ of $k[x]$ is maximal if and only if $I = (x-c)$

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Can the square of a proper ideal be equal to the ideal?

Published on 09 Apr 2026 - 19:40

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Primary decomposition of ideals

Published on 25 Mar 2026 - 14:03

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Extension of the radical of an ideal

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List Question

Decomposition of a monomial ideal

Let $R$ be a commutative ring. For $a \in R$ consider the set $(a) = \{r*a | r\in R\}$. Show that $(a) = R$ if a is a unit of $R$

Ideals of Unique Factorization Domain

Build a reduced ring starting from an ordinary one

The ideal generated by $(x,y) \cdot (x,z) \cdot (y,z)$ in $k[x,y,z]$ for a field $k$

Expressing a hypersurface of a variety as zero locus

How do I show $(f_1(x), f_2(x), ..., x-a) = (f_1(a), ..., f_r(a), x-a)$ where $a \in R$, $R$ is a commutative ring, $f_i(x) \in R[x]$

Does localization commute with taking radicals?

$(x_1, ..., x_k)$ is prime in $R[x_1, ..., x_n]$ if $R$ is an integral domain

Generator of intersection of ideals in a PID via adjunction?

Nilpotent or non-Nilpotent Jacobson Radical

For an algebraically closed field $k$, an ideal $I$ of $k[x]$ is maximal if and only if $I = (x-c)$

Can the square of a proper ideal be equal to the ideal?

Primary decomposition of ideals

Extension of the radical of an ideal

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