List questions from localization

Published on 23 Oct 2016 - 20:38

216

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Are these statements about the localization of a module true?

Published on 25 Oct 2016 - 15:33

727

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Connection between the annihilator and the localization of a module

Published on 26 Oct 2016 - 10:31

97

Views

If the restrictions of an element of $\operatorname{Spec}R$ to a cover of $\operatorname{Spec}R$ is zero, then the element is zero

Published on 26 Oct 2016 - 17:42

195

Views

$f(x)=x/1$ is not injective?

Published on 31 Oct 2016 - 1:57

22

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Why the ideal generated by $\varphi(I)$ is $IS^{-1}R$?

Published on 31 Oct 2016 - 13:43

190

Views

Understanding the definition of the fraction ring of a ring that is not a domain.

Published on 31 Oct 2016 - 14:01

1k

Views

Power of maximal ideal in the localization of $k[x,y]$ at $(x,y)$

Published on 25 Mar 2026 - 13:56

1.2k

Views

The kernel of the quotient map $R \to R[x]/(ax-1)$

Published on 03 Nov 2016 - 0:38

1.7k

Views

Group of units of localization

Published on 03 Nov 2016 - 19:53

66

Views

Abuse of notation: identifying a structure with a canonical injective image

Published on 03 Nov 2016 - 20:35

651

Views

Show that $M = 0$ iff $M_{\mathfrak{p}} = 0$ iff $M_{\mathfrak{m}} = 0$.

Published on 06 Nov 2016 - 13:56

1.8k

Views

The kernel of the localization map

Published on 26 Mar 2026 - 7:56

234

Views

Show that the following localization is a unique factorization domain

Published on 10 Nov 2016 - 17:47

220

Views

intersection of localization with the base field

Published on 25 Mar 2026 - 19:01

List Question

Sanity check - localizations are pushouts and they are pushout stable

Are these statements about the localization of a module true?

Connection between the annihilator and the localization of a module

If the restrictions of an element of $\operatorname{Spec}R$ to a cover of $\operatorname{Spec}R$ is zero, then the element is zero

$f(x)=x/1$ is not injective?

Why the ideal generated by $\varphi(I)$ is $IS^{-1}R$?

Understanding the definition of the fraction ring of a ring that is not a domain.

Power of maximal ideal in the localization of $k[x,y]$ at $(x,y)$

The kernel of the quotient map $R \to R[x]/(ax-1)$

Group of units of localization

Abuse of notation: identifying a structure with a canonical injective image

Show that $M = 0$ iff $M_{\mathfrak{p}} = 0$ iff $M_{\mathfrak{m}} = 0$.

The kernel of the localization map

Show that the following localization is a unique factorization domain

intersection of localization with the base field

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