List questions from commutative-algebra

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proof of Proposition 3.3.18 in Bruns and Herzog

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Comparing an ideal and its saturation

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Tensor product of local Artinian rings

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$J \subset I(V(J))$ where $J$ is an ideal.

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Show that $\operatorname{Hom}(S(-d),S)\cong S(d)$ where $S$ is polynomial ring?

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List Question

$I$-smoothness in Algebraic Geometry

Is the image of a morphism between affine schemes always constructible?

proof of Proposition 3.3.18 in Bruns and Herzog

Comparing an ideal and its saturation

Tensor product of local Artinian rings

Correspondence between ideals of $R$ and $D^{-1}R$

Atiyah & MacDonald on local Noetherian and Artinian rings - sanity check.

$J \subset I(V(J))$ where $J$ is an ideal.

Transcendental solution to system of equations

For a ring homomorphism, why does $f$ induces a homeomorphism from $SpecB$ onto the closed subset $V(\ker f)$ of $SpecA$.

Computing homomorphisms between extensions of modules

A condition that an algebraic set is irreducible.

Counterexample for the infinitely many primes between two primes in a Noetherian ring

Exercise of commutative algebra, rational functions.

Show that $\operatorname{Hom}(S(-d),S)\cong S(d)$ where $S$ is polynomial ring?

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