New posts in Localization

Why does $Re=S^{-1}R$?

Ideal with zero localizations at prime ideals containing it

$\mathfrak p$ be a prime ideal of a commutative ring $R$ , then $R_\mathfrak p/\mathfrak pR_\mathfrak p$ is the field of fractions of $R/\mathfrak p$?

What are some local properties?

A question about the equivalence relation on the localization of a ring.

Localization commutes with quotient

Localizations of an Artinian ring are isomorphic to quotients.

Atiyah-Macdonald problem 3.8

Why is the localization at a prime ideal a local ring?

Subrings of fraction fields