TL;DR
This paper introduces F-schemes, a new mathematical framework that generalizes schemes to include noncommutative rings, expanding the scope of algebraic geometry.
Contribution
The paper presents F-schemes as a novel extension of schemes to noncommutative rings, broadening the applicability of algebraic geometric methods.
Findings
F-schemes encompass noncommutative rings.
Extension of scheme theory to noncommutative algebra.
Potential new tools for noncommutative geometry.
Abstract
In this paper, the notion of F-schemes, a "generalization" of schemes, is introduced to cover unitary noncommutative rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology