On Continuous and Adjoint Morphisms Between Noncommutative Prime Spectra

Details On Continuous and Adjoint Morphisms Between Noncommutative Prime Spectra On Continuous and Adjoint Morphisms Between Noncommutative Prime Spectra

2004-03-12

arxiv.org/abs/math/0403204v3

Mathematics

Rings and Algebras

13 pages; AMS-TeX. Minor revisions; reference added. To appear in Proceedings of the Edinburgh Mathematical Society

Scientific paper

We study topological properties of the correspondence of prime spectra associated to a noncommutative ring homomorphism R -> S. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of Spec(R) and Spec(S); these functors arise naturally from restriction and extension of scalars. When R and S are left noetherian, adjointness occurs only for centralizing and ``nearly centralizing'' homomorphisms.

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