List questions from commutative-algebra

Published on 01 Apr 2026 - 9:32

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With B integral over subring A, homomorphism from A to algebraically closed field F can be extended to B.

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Tensor product of quotient rings

Published on 13 Apr 2026 - 7:54

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Dimensions of integral ring extensions

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If an identity in the language of rings holds for all fields, does it necessarily hold for all commutative rings?

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Quotient ring is cyclic group implies every ideal is generated by 2 elements

Published on 14 Apr 2026 - 4:54

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Is this automorphism the identity map

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Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?

Published on 25 Mar 2026 - 16:02

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What is the unmixedness theorem?

Published on 11 Apr 2026 - 2:28

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help in an example.

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$\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed

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Is quotient of a ring by a power of a maximal ideal local?

Published on 13 Apr 2026 - 16:02

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Number of maximal and prime ideals

Published on 13 Apr 2026 - 10:11

183

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Are the generators of the subgroup defining tensor products linearly independent over $\mathbb Z$?

Published on 10 Apr 2026 - 11:04

87

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Noetherian local ring, detail in theorem 1.3.16 in Liu

Published on 14 Apr 2026 - 10:26

List Question

$A_{p}$ is a field when $p$ is a minimal prime and $A$ reduced

With B integral over subring A, homomorphism from A to algebraically closed field F can be extended to B.

Tensor product of quotient rings

Dimensions of integral ring extensions

If an identity in the language of rings holds for all fields, does it necessarily hold for all commutative rings?

Quotient ring is cyclic group implies every ideal is generated by 2 elements

Is this automorphism the identity map

Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?

What is the unmixedness theorem?

help in an example.

$\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed

Is quotient of a ring by a power of a maximal ideal local?

Number of maximal and prime ideals

Are the generators of the subgroup defining tensor products linearly independent over $\mathbb Z$?

Noetherian local ring, detail in theorem 1.3.16 in Liu

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