Noncommutative Localisation

Dominic Bush-Hipwood


We all know how we can build the rationals out of the integers. This construction can be easily generalised to commutative rings. It's therefore natural to ask 'Can we create rings of fractions in the noncommutative setting?'. We will see that there are a few more subtleties involved, but ultimately we can do it (provided the ring is sufficiently nice). There will be plenty of examples and the ring theory we will see will be basic.

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