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One case for non-commutative rings where localization has a clear interest is for rings of differential operators. It has the interpretation, for example, of adjoining a formal inverse D<sup>-1</sup> for a differentiation operator D. This is done in many contexts in methods for [[differential equation]]s. There is now a large mathematical theory about it, named ''microlocalization'', connecting with numerous other branches. The ''micro-'' tag is to do with connections with Fourier theory, in particular.
See also: [[Localization of a module]], [[localization of a category]].
[[Category:Ring theory]]
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