List questions from commutative-algebra

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Is this module noetherian?

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240

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2-dimensional Cohen-Macaulay domain

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Prime ideal is contraction of prime ideal iff it's saturated

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130

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For some finitely many nonzero prime ideals, the contraction and extension of their product is zero

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608

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If the localization of a ring is a field, then the ring is an integral domain?

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Possible examples where the Zero Divisor Conjecture does not hold

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Exercise from Kaplansky's Commutative Rings and Eakin-Nagata Theorem

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A prime ideal in the intersection of powers of another ideal

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512

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Question about completion of DVR.

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Residue field of a local ring as field extension

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149

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Finding a particular principal open subset of $Spec R$

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190

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One dimensional noetherian domain

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1.2k

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What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

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Prove that if the induced homomorphism $M/\mathfrak aM \to N/\mathfrak aN$ is surjective, then $f$ it's surjective.

Published on 16 Apr 2026 - 6:13

List Question

A quotient of a regular local ring may not be regular

Is this module noetherian?

2-dimensional Cohen-Macaulay domain

Prime ideal is contraction of prime ideal iff it's saturated

For some finitely many nonzero prime ideals, the contraction and extension of their product is zero

If the localization of a ring is a field, then the ring is an integral domain?

Possible examples where the Zero Divisor Conjecture does not hold

Exercise from Kaplansky's Commutative Rings and Eakin-Nagata Theorem

A prime ideal in the intersection of powers of another ideal

Question about completion of DVR.

Residue field of a local ring as field extension

Finding a particular principal open subset of $Spec R$

One dimensional noetherian domain

What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

Prove that if the induced homomorphism $M/\mathfrak aM \to N/\mathfrak aN$ is surjective, then $f$ it's surjective.

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