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taking noncommutative stack quotients). For example, noncommutative algebraic geometry is supposed to extend a notion of an algebraic scheme by suitable...

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces...

several such affine schemes, in analogy to the way of constructing a manifold by gluing together the charts of an atlas. Noncommutative rings resemble rings...

In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are...

theorem states a scheme X can be recovered from the category of quasi-coherent sheaves on X. The theorem is a starting point for noncommutative algebraic geometry...

group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they...

that if an ideal of a noncommutative ring R satisfies the commutative definition of prime, then it also satisfies the noncommutative version. An ideal P...

A. L. Rosenberg, Noncommutative schemes, Compositio Mathematica 112 (1998) 93–125, doi; Underlying spaces of noncommutative schemes, preprint MPIM2003-111...

In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived...

of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative...

the combinatorics of simplicial complexes. F1 has been connected to noncommutative geometry and to a possible proof of the Riemann hypothesis. In 1957...

quiver Toric variety Derived noncommutative algebraic geometry - Quivers help encode the data of derived noncommutative schemes Derksen, Harm; Weyman, Jerzy;...

1515/crelle-2013-0027, MR 3331729 Orlov, Dmitri (2016), "Smooth and proper noncommutative schemes and gluing of DG categories", Advances in Mathematics, 302: 59–105...

algebraic variety, and the ring of integers of a number field. Examples of noncommutative rings include the ring of n × n real square matrices with n ≥ 2, group...

external characterizations. The following equivalences appear in many noncommutative algebra texts such as Anderson & Fuller 1992, §15, Isaacs 1994, §13B...

Dylan G.L. Allegretti, Differential Forms on Noncommutative Spaces. An elementary introduction to noncommutative geometry which uses Hochschild homology to...

Generalizing to non-commutative C*-algebras yields noncommutative topology. Scheme (mathematics) Projective scheme Spectrum of a matrix Serre's theorem on affineness...

theory; Abstract geometry, including algebraic geometry, categorical noncommutative geometry, etc. Quantization related to category theory, in particular...

one hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various...

quasi-separated scheme can be recovered from the category of quasi-coherent sheaves on it. The theorem is taken as a starting point for noncommutative algebraic...