List questions from commutative-algebra

Published on 25 Mar 2026 - 6:10

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Determining if a curve is or is not a variety

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209

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Example of a ring with unique prime ideal of a given height

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172

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Properties of intersection of subalgebras

Published on 01 Apr 2026 - 5:05

197

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Fixed points of an endomorphism of a ring

Published on 26 Mar 2026 - 1:10

853

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If the direct sum of a module with a free module is free, then that module is zero

Published on 25 Mar 2026 - 3:20

141

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Closed, irreducible subset of an affine variety

Published on 17 Sep 2018 - 12:29

168

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Is $Y=V(\cos(t),\sin(t),t)\subset k^3$ a variety?

Published on 25 Mar 2026 - 6:12

761

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The ring of formal series in a variable $R=k[[x]]$ is a local ring, where the ideal maximal $m$ is the ideal of all series with term independent zero

Published on 29 Mar 2026 - 10:08

454

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Polynomial ring as a (complete) metric space

Published on 27 Mar 2026 - 6:51

327

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An $R$-module $M$ that is not finitely generated but $M/xM$ is finitely generated.

Published on 17 Sep 2018 - 22:33

221

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When a homogeneous ideal is written as a product of two ideals, then each of two ideals is homogeneous?

Published on 23 Mar 2026 - 4:43

81

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If $P$ is a projective module, then there exist a free module $F$ with $P\bigoplus F$ is free.

Published on 18 Sep 2018 - 7:37

153

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How do we know that the only polynomials $f$ satisfying $f(\lambda x_0,\ldots,\lambda x_n) = f( x_0,\ldots,x_n) $ are the constant polynomials?

Published on 26 Mar 2026 - 6:30

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Absolutely Flat Ring

Published on 26 Mar 2026 - 23:43

List Question

It is the set $V(y-\sin(x))\subset k^2$ a variety?

Determining if a curve is or is not a variety

Example of a ring with unique prime ideal of a given height

Properties of intersection of subalgebras

Fixed points of an endomorphism of a ring

If the direct sum of a module with a free module is free, then that module is zero

Closed, irreducible subset of an affine variety

Is $Y=V(\cos(t),\sin(t),t)\subset k^3$ a variety?

The ring of formal series in a variable $R=k[[x]]$ is a local ring, where the ideal maximal $m$ is the ideal of all series with term independent zero

Polynomial ring as a (complete) metric space

An $R$-module $M$ that is not finitely generated but $M/xM$ is finitely generated.

When a homogeneous ideal is written as a product of two ideals, then each of two ideals is homogeneous?

If $P$ is a projective module, then there exist a free module $F$ with $P\bigoplus F$ is free.

How do we know that the only polynomials $f$ satisfying $f(\lambda x_0,\ldots,\lambda x_n) = f( x_0,\ldots,x_n) $ are the constant polynomials?

Absolutely Flat Ring

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