List questions from maximal-and-prime-ideals

Published on 25 Mar 2026 - 4:35

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Inclusion of ideals in \mathbb{C}[x,y]

Published on 30 Jul 2019 - 15:51

430

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Points on the "conic" $\mathbb{R}[x, y] / (x^2 + y^2 + 1) $

Published on 01 Aug 2019 - 2:50

117

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Find the rings such that $I^s=\{0\}$ for any maximal ideal $I$ where $s$ is the characteristic.

Published on 01 Aug 2019 - 6:55

225

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$x+ I \subset p_1 \cup \cdots \cup p_n$ then for some $i$, $x + I \subset p_i.$

Published on 02 Aug 2019 - 14:28

189

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Prime ideals in R[x] having the same contraction in R

Published on 25 Mar 2026 - 13:54

131

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Find a ring $R$ with a chain of prime ideals of length 2008.

Published on 06 Aug 2019 - 16:05

712

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Ring of integers of quadratic field extension, every element with prime norm is a prime

Published on 06 Aug 2019 - 23:13

1.6k

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Every prime ideal in $\mathbb{Z}[x]$ is generated by at most two elements

Published on 08 Aug 2019 - 20:36

1.1k

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Must a ring (commutative, with 1), in which every non-zero ideal is prime, be a field?

Published on 08 Aug 2019 - 22:05

1.4k

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$\mathbb{C}[x,y,z]/(xy-z^2)$ is not a field

Published on 11 Aug 2019 - 19:45

52

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localizations of $k[x, y, z]/(x^2 + y^2 + z^2)$

Published on 25 Mar 2026 - 17:20

99

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Meaning of the notation $M_p$

Published on 18 Aug 2019 - 9:47

64

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$\psi:\text{spec}(R/J)\to\text{spec}(R)$ is the natural mapping. Prove that if $\psi(Z)$ is Zariski closed then $Z$ is Zariski closed

Published on 22 Aug 2019 - 17:03

952

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Prove that $ \langle x^2+y^2+z^2 \rangle $ is a prime ideal of $ \mathbb{R}[x, y, z]$

Published on 24 Aug 2019 - 5:44

List Question

Condition for Projective Variety

Inclusion of ideals in \mathbb{C}[x,y]

Points on the "conic" $\mathbb{R}[x, y] / (x^2 + y^2 + 1) $

Find the rings such that $I^s=\{0\}$ for any maximal ideal $I$ where $s$ is the characteristic.

$x+ I \subset p_1 \cup \cdots \cup p_n$ then for some $i$, $x + I \subset p_i.$

Prime ideals in R[x] having the same contraction in R

Find a ring $R$ with a chain of prime ideals of length 2008.

Ring of integers of quadratic field extension, every element with prime norm is a prime

Every prime ideal in $\mathbb{Z}[x]$ is generated by at most two elements

Must a ring (commutative, with 1), in which every non-zero ideal is prime, be a field?

$\mathbb{C}[x,y,z]/(xy-z^2)$ is not a field

localizations of $k[x, y, z]/(x^2 + y^2 + z^2)$

Meaning of the notation $M_p$

$\psi:\text{spec}(R/J)\to\text{spec}(R)$ is the natural mapping. Prove that if $\psi(Z)$ is Zariski closed then $Z$ is Zariski closed

Prove that $ \langle x^2+y^2+z^2 \rangle $ is a prime ideal of $ \mathbb{R}[x, y, z]$

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