This paper concerns contravariant functors from the category of rings to the category of sets who... more This paper concerns contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M _n (C) for n⩾ 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gel'fand spectrum functor for C*-algebras is ...
This paper concerns contravariant functors from the category of rings to the category of sets who... more This paper concerns contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M _n (C) for n⩾ 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gel'fand spectrum functor for C*-algebras is ...
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Papers by Manuel Xicoténcatl Barrón Reyes