List questions from maximal-and-prime-ideals

Published on 04 Apr 2020 - 7:16

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Show that every prime ideal of A (UFD) is generated by a set of prime elements

Published on 25 Mar 2026 - 23:24

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Cyclic Modules over a PID

Published on 28 Mar 2026 - 13:22

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Can a maximal ideal of $k[x, y] / (f)$ be embedded as a maximal ideal of $k'[x, y] / (f)$ where $k'$ is the algebraic closure of $k$?

Published on 29 Mar 2026 - 22:09

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Given prime ideal $P$ of ring $R$, does $RrR\subset P$ imply $r\in P$ for $r\in R$? (Hungerford)

Published on 25 Mar 2026 - 4:43

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Quotient ring is Prime iff the ideal is prime ideal

Published on 09 Apr 2020 - 9:42

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Prime and Maximal Ideals of $\mathbb{Z}[\sqrt{-10}]$

Published on 22 Mar 2026 - 6:42

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Atiyah MacDonald Commutative algebra page 3

Published on 09 Apr 2020 - 18:17

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$M$ maximal iff $\bar{M}$ is maximal

Published on 11 Apr 2020 - 13:15

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Prove that radical of an ideal is contained in the Jacobson of the ideal

Published on 11 Apr 2020 - 15:20

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Why is the ideal $\langle x^2, 2\rangle$ of $\mathbb{Z}[x]$ a primary ideal?

Published on 11 Apr 2020 - 17:07

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Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

Published on 28 Mar 2026 - 11:33

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Atiyah Macdonald commutative algebra page 4

Published on 12 Apr 2020 - 9:20

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Is there a way to order the maximal ideals of the ring of integers? Is there an order structure to maximal ideals?

Published on 12 Apr 2020 - 15:19

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Is there any maximal ideal that contains the unity element of a ring?

Published on 14 Apr 2020 - 7:41

List Question

Is $\mathbb{Z}_3[x] / \langle x^2+x+1 \rangle $ an integral domain?

Show that every prime ideal of A (UFD) is generated by a set of prime elements

Cyclic Modules over a PID

Can a maximal ideal of $k[x, y] / (f)$ be embedded as a maximal ideal of $k'[x, y] / (f)$ where $k'$ is the algebraic closure of $k$?

Given prime ideal $P$ of ring $R$, does $RrR\subset P$ imply $r\in P$ for $r\in R$? (Hungerford)

Quotient ring is Prime iff the ideal is prime ideal

Prime and Maximal Ideals of $\mathbb{Z}[\sqrt{-10}]$

Atiyah MacDonald Commutative algebra page 3

$M$ maximal iff $\bar{M}$ is maximal

Prove that radical of an ideal is contained in the Jacobson of the ideal

Why is the ideal $\langle x^2, 2\rangle$ of $\mathbb{Z}[x]$ a primary ideal?

Isn't $I$ a maximal ideal in $\Bbb Z_{11} [X]$?

Atiyah Macdonald commutative algebra page 4

Is there a way to order the maximal ideals of the ring of integers? Is there an order structure to maximal ideals?

Is there any maximal ideal that contains the unity element of a ring?

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