List questions from localization | MathQa

Isomorphism of Localization of $A_\mathfrak{p}$ and $A_\mathfrak{q}$

Published on 29 Dec 2024 - 18:44

Serre quotient category

Published on 12 Jan 2025 - 17:34

$R=\{a/b: a,b \in \mathbb{Z}$ and $b$ is odd}. Show that the ring $R$ is a PID.

Published on 12 Jan 2025 - 23:46

Localization of a one-dimensional noetherian integral domain

Published on 12 Jan 2025 - 9:23

Prove that $a\mathbb{Z} \cap \mathbb{Z} \backslash p\mathbb{Z} \neq \varnothing \iff a\mathbb{Z}_{(p)}=\mathbb{Z}_{(p)}$

Published on 29 Dec 2024 - 6:49

Prove that there exists a unique homomorphism of $\mathbb{Z}_{(p)}$-modules $\beta:M_p \rightarrow N$ such that $\beta(m/r)=\frac{1}{r}\alpha(m)$.

Published on 12 Jan 2025 - 9:35

Show that each element of $K$ can be written as $\frac{b}{a}$ where, $b\in B, a\in A$

Published on 12 Jan 2025 - 9:35

When is localization a quotient?

Published on 12 Jan 2025 - 22:59

Is every local quasi-finite morphism finite?

Published on 30 Dec 2024 - 15:55

A Notation in Matsumura's Commutative Algebra

Published on 12 Jan 2025 - 9:35