List questions from commutative-algebra

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Commuting Derivations on Regular Local $k$-algebra

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Help with proof in Hartshorne concerning points in a product scheme being regular in codim 1

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roots of ring of polynomials; ex 2.21 in Allen and Stevens Commutative Algebra

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Reference request - infinite ramification theory

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Divided power envelope and polynomial rings

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If p is a prime ideal of P then Id( R/P ) = { P , P+1 }

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Show that the algebraic subsets of $\mathbb{A}^1(k)$ are just the finite subsets, together with $\mathbb{A}^1(k)$ itself

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Showing all finite subsets of $\mathbb{A}^n(k)$ are algebraic, and is it possible to sample from the resulting ideal?

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prime ideals of $\mathbb{R}[X,Y]/(X-Y^2,X+Y)$

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Irreducible polynomials have no zeroes with multiplicity $\geq 1$

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Jacobson local ring that is not Artinian

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Monomial ideal which is not saturated.

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g.c.d. and l.c.m. in $\mathbb{Z}[\sqrt{-3}]$

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Which polynomials are "transitive" with respect to $\mathbb{Z}/r\mathbb{Z}$?

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List Question

A finitely-generated ring over the integers modulo a max ideal is necessarily a finite field

Commuting Derivations on Regular Local $k$-algebra

Help with proof in Hartshorne concerning points in a product scheme being regular in codim 1

roots of ring of polynomials; ex 2.21 in Allen and Stevens Commutative Algebra

Reference request - infinite ramification theory

Divided power envelope and polynomial rings

If p is a prime ideal of P then Id( R/P ) = { P , P+1 }

Show that the algebraic subsets of $\mathbb{A}^1(k)$ are just the finite subsets, together with $\mathbb{A}^1(k)$ itself

Showing all finite subsets of $\mathbb{A}^n(k)$ are algebraic, and is it possible to sample from the resulting ideal?

prime ideals of $\mathbb{R}[X,Y]/(X-Y^2,X+Y)$

Irreducible polynomials have no zeroes with multiplicity $\geq 1$

Jacobson local ring that is not Artinian

Monomial ideal which is not saturated.

g.c.d. and l.c.m. in $\mathbb{Z}[\sqrt{-3}]$

Which polynomials are "transitive" with respect to $\mathbb{Z}/r\mathbb{Z}$?

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