Monthly Archives: July 2012

An elementary result on noncommutative rings.

Let R be a (noncommutative) ring with identity, such that there are elements u and v with u v = 1.  Then the following are equivalent: u w = 0 for some nonzero w. u is not a unit. u … Continue reading

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The cross-ratio

Here is a nice invariant from classical geometry that I’d never heard of before today. The action of on restricts to an action on ; this is all that a Möbius transformation really is.  Now  is four-dimensional, but there’s a … Continue reading

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