Localization math：5.1 Localization (Commutative Algebra and Algebraic Geometry)
5.1 Localization (Commutative Algebra and Algebraic Geometry)
6. Localization
https://agag-gathmann.math.rpt
Localization is a very powerful technique in commutative algebra that often allows to reduce ques- tions on rings and modules to a union of smaller “local” ...
Category
https://en.wikipedia.org
In mathematics, specifically algebraic geometry and its applications, localization is a way of studying an algebraic object at a prime.
Localization
http://math.stanford.edu
The ring S−1A is called a localization of A. This terminology arises from consideration of rings of continuous functions, with values, say, in a field. If A is ...
Localization (commutative algebra)
https://en.wikipedia.org
The term localization originates in the general trend of modern mathematics to study geometrical and topological objects locally, that is in terms of their ...
Localization
https://mathworld.wolfram.com
An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, ...
localization of a ring in nLab
https://ncatlab.org
Often one inverts elements in a left or right Ore subset S ⊂ R S-subset R in which case the localized ring is expressed by fractions as naively ...
ring theory
https://math.stackexchange.com
The universal characterisation you provided is just a property that is only a piece of the true universal property. You can think of it as ...
Section 10.9 (00CM)
https://stacks.math.columbia.e
1. Let R be a ring, S a subset of R. · 2. This ring is called the localization of A with respect to S. · 3. Let f : A -to B be a ring map that sends every element ...
What is the importance of localization in algebraic geometry?
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One of the philosophical points of algebraic geometry is to study not the geometric object itself, but the set of functions on it.