Obstructing extensions of the functor Spec to noncommutative rings

Details Obstructing extensions of the functor Spec to noncommutative rings Obstructing extensions of the functor Spec to noncommutative rings

2011-01-11

arxiv.org/abs/1101.2239v3

Mathematics

Rings and Algebras

23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline

Scientific paper

In this paper we study 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 Gelfand spectrum functor for C*-algebras is also proved.

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