List questions from commutative-algebra

Published on 28 Mar 2014 - 15:00

989

Views

A monomial ideal, $I =\langle xy, xz, yz\rangle$, is radical

Published on 11 Apr 2026 - 18:49

260

Views

When does coprimality carry over to the base ring in an integral extension of Dedekind domains?

Published on 12 Apr 2026 - 21:40

758

Views

Generators for (radical) ideal of product of affine varieties

Published on 10 Apr 2026 - 18:34

57

Views

Grading and commutators

Published on 14 Apr 2026 - 2:48

798

Views

Ring homomorphism with field as image, is the pre-image also a field?

Published on 09 Apr 2026 - 6:02

619

Views

Every irreducible element is prime: always holds under surjective ring homomorphism?

Published on 25 Mar 2026 - 15:47

108

Views

Topological closure of ideal in $A[[T]]$ - Proposition 1.3.7 in Liu

Published on 12 Apr 2026 - 19:16

871

Views

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

Published on 14 Apr 2026 - 5:13

515

Views

Techniques for showing an ideal in $k[x_1,\ldots,x_n]$ is prime

Published on 13 Apr 2026 - 16:45

5k

Views

Intersection of all maximal ideals containing a given ideal

Published on 30 Mar 2014 - 19:48

279

Views

A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$

Published on 11 Apr 2026 - 2:37

278

Views

is the hilbert polynomial integer-valued everywhere?

Published on 13 Apr 2026 - 7:56

367

Views

Showing the set of diagonalizable matrices is constructible

Published on 14 Apr 2026 - 3:27

2.2k

Views

If the tensor product of two modules is free of finite rank, then the modules are finitely generated and projective

Published on 26 Mar 2026 - 8:02

List Question

Square of tensor product

A monomial ideal, $I =\langle xy, xz, yz\rangle$, is radical

When does coprimality carry over to the base ring in an integral extension of Dedekind domains?

Generators for (radical) ideal of product of affine varieties

Grading and commutators

Ring homomorphism with field as image, is the pre-image also a field?

Every irreducible element is prime: always holds under surjective ring homomorphism?

Topological closure of ideal in $A[[T]]$ - Proposition 1.3.7 in Liu

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

Techniques for showing an ideal in $k[x_1,\ldots,x_n]$ is prime

Intersection of all maximal ideals containing a given ideal

A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$

is the hilbert polynomial integer-valued everywhere?

Showing the set of diagonalizable matrices is constructible

If the tensor product of two modules is free of finite rank, then the modules are finitely generated and projective

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