List questions from modules

Published on 11 Apr 2026 - 18:33

295

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Proving that $0 \rightarrow \Bbb Z \rightarrow \Bbb Q \rightarrow \Bbb Q / \Bbb Z \rightarrow 0$ does not split.

Published on 25 Mar 2026 - 14:23

186

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Extending scalars to Quotient ring

Published on 10 Apr 2026 - 9:15

118

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If $\widehat{M}$ is a free $\widehat{R}$-module, then $M$ is a free $R$-module, $R$ is a Zariski ring.

Published on 25 Mar 2026 - 4:41

56

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If $S$ is a free $R$-algebra, then no element of $S$ is integral over $R$? And other questions.

Published on 13 Apr 2026 - 2:12

162

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Suppose $k$ is a field. Let $\frac{\bar x}{\bar y} \in Frac(k[x,y]/(x^2-y^3))$. How is $k[\frac{\bar x}{\bar y}]$ a UFD?

Published on 13 Jul 2020 - 20:56

109

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Modifying $\frac{\prod_\alpha A_\alpha}{\prod_\alpha B_\alpha}\simeq \prod_\alpha\frac{A_\alpha}{B_\alpha}$ for direct sums

Published on 26 Mar 2026 - 17:37

101

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Geometric meaning of Koszul (co)homology?

Published on 13 Apr 2026 - 8:26

102

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Free resolutions reference request

Published on 14 Jul 2020 - 3:45

90

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Linear independence of the basis of $F/IF$

Published on 14 Jul 2020 - 7:46

425

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Projective graded modules

Published on 25 Mar 2026 - 21:30

176

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An $A$-algebra $B$ carries the same data as a ring map $A \rightarrow B$

Published on 14 Jul 2020 - 15:47

156

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Definition of a module over a Lie algebra

Published on 11 Apr 2026 - 5:02

155

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Is $S^{-1}R$ a free $R$-module?

Published on 28 Mar 2026 - 1:46

187

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Classification of finite algebras over a PID.

Published on 10 Apr 2026 - 14:50

List Question

Number Theory: Modular Arithmetic

Proving that $0 \rightarrow \Bbb Z \rightarrow \Bbb Q \rightarrow \Bbb Q / \Bbb Z \rightarrow 0$ does not split.

Extending scalars to Quotient ring

If $\widehat{M}$ is a free $\widehat{R}$-module, then $M$ is a free $R$-module, $R$ is a Zariski ring.

If $S$ is a free $R$-algebra, then no element of $S$ is integral over $R$? And other questions.

Suppose $k$ is a field. Let $\frac{\bar x}{\bar y} \in Frac(k[x,y]/(x^2-y^3))$. How is $k[\frac{\bar x}{\bar y}]$ a UFD?

Modifying $\frac{\prod_\alpha A_\alpha}{\prod_\alpha B_\alpha}\simeq \prod_\alpha\frac{A_\alpha}{B_\alpha}$ for direct sums

Geometric meaning of Koszul (co)homology?

Free resolutions reference request

Linear independence of the basis of $F/IF$

Projective graded modules

An $A$-algebra $B$ carries the same data as a ring map $A \rightarrow B$

Definition of a module over a Lie algebra

Is $S^{-1}R$ a free $R$-module?

Classification of finite algebras over a PID.

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