# February 18, 2010

## Noncommutative Zariski topology?

There are a lot of discussions on mathoverflow on Zariski topology in commutative algebraic geometry. What I want to do is to see whether we can formulate noncommutative version Zariski topology which should play roles to cover noncommutative schemes.

First,we took a look at the usual Zariski topology. If is a commutative ring(-algebra), then the open set of Zariski topology on is . Actually, if we make more precise description: we take as radical ideal. Then following the fact that:

.

Radical ideal determines the (open)schemes uniquely.

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