On the Connectedness of the Spectrum of Forcing Algebras

We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplificati...

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Veröffentlicht in:Revista colombiana de matemáticas 2014-06, Vol.48 (1), p.1-19
Hauptverfasser: BRENNER, HOLGER, GÓMEZ-RAMÍREZ, DANNY DE JESÚS
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description We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplifications when the base ring is local, or one--dimensional, or factorial. Besides, we discuss whether the connectedness of forcing algebras is a local property. Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the corresponding forcing morphism.
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title On the Connectedness of the Spectrum of Forcing Algebras
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