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ON CONTINUOUS AND ADJOINT MORPHISMS BETWEEN NON-COMMUTATIVE PRIME SPECTRA

Published online by Cambridge University Press:  30 May 2006

Edward S. Letzter
Edward S. Letzter
Affiliation:
Department of Mathematics, Wachman Hall, 1805 North Broad Street, Temple University, Philadelphia, PA 19122, USA ([email protected])
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Abstract

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We study topological properties of the correspondence of prime spectra associated with a non-commutative ring homomorphism $R\rightarrow S$. 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.

Keywords

Primary 16D2516S20non-commutative ringring extensionprime ideal
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 367 - 381
Copyright
Copyright © Edinburgh Mathematical Society 2006