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...
- Autores:
-
Brenner, Holger
Gómez-Ramírez, Danny de Jesús
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2014
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/49345
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/49345
http://bdigital.unal.edu.co/42802/
- Palabra clave:
- Álgebra de forzado
conexidad
clausura entera
13B22
14A15
14R25
54D05
Forcing algebra
Connectedness
Integral closure
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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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