Every ring can be recovered from a new topological object, its noncommutative spectrum, extending the classical duality between commutative rings and affine schemes.
Balmer, Descent in triangulated categories , Math
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Noncommutative Gelfand Duality: the algebraic case
Every ring can be recovered from a new topological object, its noncommutative spectrum, extending the classical duality between commutative rings and affine schemes.