List questions from maximal-and-prime-ideals

Published on 08 Apr 2017 - 6:27

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Indecomposable injective modules

Published on 26 Mar 2026 - 17:34

29

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Properties of an ideal located between two prime ideals.

Published on 02 Feb 2023 - 9:14

35

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Which of the following statements are correct regarding $I(x)?$

Published on 11 Feb 2023 - 14:31

380

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Show that an ideal $M \ne R$ in a commutative ring $R$ with unity is maximal if and only if for every $r∈R−M$, there exists $x∈R$ such that $1_R−rx∈M$

Published on 16 Feb 2023 - 1:44

95

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Justify the use of Zorn's Lemma in a proof

Published on 26 Mar 2026 - 13:00

28

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Let $R$ be an integral domain. Let $I$ and $J$ be nonzero prime ideals such that $I\subsetneq J$. If $I$ is principal, show that $J$ is not principal.

Published on 17 Feb 2023 - 6:14

117

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Independence complex of a prime ideal is a matroid

Published on 25 Mar 2026 - 14:05

52

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Understanding a lemma about minimal prime ideals (from McCoy's Rings and Ideals).

Published on 19 Feb 2023 - 16:23

55

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Localization in power series

Published on 25 Mar 2026 - 15:48

39

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Dimension of $(A[[X]])_\mathfrak{m} \geq k+1$, regular ring, chain of prime ideals

Published on 25 Mar 2026 - 6:06

95

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Chebotarev's Density Theorem, Equidistribution of Prime Ideals, and Class-Field Theory

Published on 27 Mar 2026 - 0:59

116

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Prime $\frak p\subset q\implies\exists$ prime $\frak p_1,q_1:p\subseteq p_1\subset q_1\subseteq q$ with no prime ideals between $\frak p_1,q_1$

Published on 22 Feb 2023 - 22:08

92

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Radicals ideals equal in field extension

Published on 24 Feb 2023 - 18:14

43

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Stone's criterion for distributive lattices

Published on 30 Mar 2026 - 4:38

List Question

Maximal ideals of C(X) requires compactness of X

Indecomposable injective modules

Properties of an ideal located between two prime ideals.

Which of the following statements are correct regarding $I(x)?$

Show that an ideal $M \ne R$ in a commutative ring $R$ with unity is maximal if and only if for every $r∈R−M$, there exists $x∈R$ such that $1_R−rx∈M$

Justify the use of Zorn's Lemma in a proof

Let $R$ be an integral domain. Let $I$ and $J$ be nonzero prime ideals such that $I\subsetneq J$. If $I$ is principal, show that $J$ is not principal.

Independence complex of a prime ideal is a matroid

Understanding a lemma about minimal prime ideals (from McCoy's Rings and Ideals).

Localization in power series

Dimension of $(A[[X]])_\mathfrak{m} \geq k+1$, regular ring, chain of prime ideals

Chebotarev's Density Theorem, Equidistribution of Prime Ideals, and Class-Field Theory

Prime $\frak p\subset q\implies\exists$ prime $\frak p_1,q_1:p\subseteq p_1\subset q_1\subseteq q$ with no prime ideals between $\frak p_1,q_1$

Radicals ideals equal in field extension

Stone's criterion for distributive lattices

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