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"pi"mp

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In my very naive understanding of algebraic geometry, I get the impression that it's written in language of commutative algebra and the main theorem (at least at the basic level) is Hilbert's Nullstellensatz. I'm curious if there's an analog of the Nullstellensatz for non-commutative algebra/geometry?

What I'm envisioning would be a correspondence between some operator/matrix algebra and a "fuzzy" geometry.

Thanks!