# Category: Localization (mathematics)

Semi-local ring
In mathematics, a semi-local ring is a ring for which R/J(R) is a semisimple ring, where J(R) is the Jacobson radical of R. The above definition is satisfied if R has a finite number of maximal right
Localization of a topological space
In mathematics, well-behaved topological spaces can be localized at primes, in a similar way to the localization of a ring at a prime. This construction was described by Dennis Sullivan in 1970 lectur
Local ring
In abstract algebra, more specifically ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defin
Hasse principle
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to pie
Valuation ring
In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F, at least one of x or x−1 belongs to D. Given a field F, if D is a subring of F
Localization of a category
In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to become isomorphisms. This is formally similar to th
Localization (commutative algebra)
In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/
Local analysis
In mathematics, the term local analysis has at least two meanings, both derived from the idea of looking at a problem relative to each prime number p first, and then later trying to integrate the info
Discrete valuation ring
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an integral domain R which satisfies any one of the