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 |
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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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