On the connectedness of the spectrum of forcing algebras

Holger Brenner; Danny Gomez-Ramirez

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arXiv · 1211.2625

On the connectedness of the spectrum of forcing algebras

Holger Brenner·Danny Gomez-Ramirez

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Abstract

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 is a local property. Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the forcing algebra

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Holger Brenner, Danny Gomez-Ramirez. 2012-11-12. On the connectedness of the spectrum of forcing algebras. https://arxiv.org/abs/1211.2625

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