List questions from commutative-algebra

Published on 08 Aug 2019 - 9:16

98

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Dimension of $R/\mathfrak{p}$ is less than dimension of $R$?

Published on 27 Mar 2026 - 20:21

241

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A strong converse to Hilbert's basis theorem

Published on 08 Aug 2019 - 12:00

797

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Non-Noetherian one-dimensional domain with a finitely generated maximal ideal

Published on 11 Apr 2026 - 23:32

1.1k

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Must a ring (commutative, with 1), in which every non-zero ideal is prime, be a field?

Published on 29 Mar 2026 - 18:50

56

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Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

Published on 25 Mar 2026 - 12:52

74

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Linear independent set of the right cardinality is a basis.

Published on 25 Mar 2026 - 13:34

396

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Proving the Generalized Bezout Theorem

Published on 26 Mar 2026 - 9:16

248

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Blow up algebras

Published on 11 Apr 2026 - 4:34

119

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$k[x_1,...,x_n]/I$ is an Artinian ring if and only if $k[x_1,...,x_n]/I$ is of finite dimension as $k$ vector space. ($k$ is algebraically closed)

Published on 12 Apr 2026 - 1:20

28

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$p\circ h\in I(X)$ if and only if $p\in I(\overline{h(X)})$?

Published on 10 Apr 2026 - 17:24

94

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What does it mean to say a functor is represented by $(X,a)$?

Published on 10 Apr 2026 - 4:31

135

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Determine all the prime ideals of $\Bbb Z[x]$ (maybe a different method)

Published on 12 Apr 2026 - 1:19

237

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Tor$^{R}_{n+1}(k,k)=0$ implies Pd$_RM\leq n$ for any $R$-module $M$?

Published on 25 Mar 2026 - 17:22

60

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What is the right way to look at tensor products?

Published on 12 Apr 2026 - 3:15

List Question

On symmetric algebra of finite dimensional vector space and its dual

Dimension of $R/\mathfrak{p}$ is less than dimension of $R$?

A strong converse to Hilbert's basis theorem

Non-Noetherian one-dimensional domain with a finitely generated maximal ideal

Must a ring (commutative, with 1), in which every non-zero ideal is prime, be a field?

Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

Linear independent set of the right cardinality is a basis.

Proving the Generalized Bezout Theorem

Blow up algebras

$k[x_1,...,x_n]/I$ is an Artinian ring if and only if $k[x_1,...,x_n]/I$ is of finite dimension as $k$ vector space. ($k$ is algebraically closed)

$p\circ h\in I(X)$ if and only if $p\in I(\overline{h(X)})$?

What does it mean to say a functor is represented by $(X,a)$?

Determine all the prime ideals of $\Bbb Z[x]$ (maybe a different method)

Tor$^{R}_{n+1}(k,k)=0$ implies Pd$_RM\leq n$ for any $R$-module $M$?

What is the right way to look at tensor products?

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