List questions from commutative-algebra

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Applications of powerful theorems in Bruns -Herzog's book "Cohen-Macaulay Rings"

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Choice of ideal so that localisation of a module must be free?

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If $\alpha$ is $R$-linear epimorphism, $\alpha$ is isomorphism.

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Continuity of induced map between spectra under constructible topology (Atiyah-Macdonald, Chapter 3, Exercise 29)

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How to show that $(Y- X^2, Z - X^3) \subseteq k[X,Y,Z]$ is a prime ideal?

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A problem involving ideals and prime ideals.

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Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$

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Looking for a commutative ring satisfying certain conditions

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Computing irreducible components of algebraic set

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253

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Singular points query

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$\mathbb{C}[x,y]/(f,g)$ is an artinian ring, if $\gcd(f,g)=1$.

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Computing the radical of an ideal

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intersection multiplicity at non-zero point

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Isomorphism between two $K$-algebras

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List Question

Inequality amongst projective dimensions!?

Applications of powerful theorems in Bruns -Herzog's book "Cohen-Macaulay Rings"

Choice of ideal so that localisation of a module must be free?

If $\alpha$ is $R$-linear epimorphism, $\alpha$ is isomorphism.

Continuity of induced map between spectra under constructible topology (Atiyah-Macdonald, Chapter 3, Exercise 29)

How to show that $(Y- X^2, Z - X^3) \subseteq k[X,Y,Z]$ is a prime ideal?

A problem involving ideals and prime ideals.

Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$

Looking for a commutative ring satisfying certain conditions

Computing irreducible components of algebraic set

Singular points query

$\mathbb{C}[x,y]/(f,g)$ is an artinian ring, if $\gcd(f,g)=1$.

Computing the radical of an ideal

intersection multiplicity at non-zero point

Isomorphism between two $K$-algebras

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