Abstract

BRENNER, HOLGER  and  GOMEZ-RAMIREZ, DANNY DE JESÚS. On the Connectedness of the Spectrum of Forcing Algebras. Rev.colomb.mat. [online]. 2014, vol.48, n.1, pp.1-19. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v48n1.45192.

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.

Keywords : Forcing algebra; Connectedness; Integral closure.

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