Dagger closure in regular rings containing a field
Autor(en): | Brenner, Holger Staebler, Axel |
Stichwörter: | COHEN-MACAULAY ALGEBRAS; Dagger closure; INTEGRAL-EXTENSIONS; Mathematics; Regular rings; TIGHT CLOSURE | Erscheinungsdatum: | 2012 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | JOURNAL OF ALGEBRA | Volumen: | 370 | Startseite: | 176 | Seitenende: | 185 | Zusammenfassung: | We prove that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in positive characteristic under some mild finiteness conditions. Furthermore, we prove that dagger closure is always contained in solid closure and that the forcing algebra for an element contained in dagger closure is parasolid. (C) 2012 Elsevier Inc. All rights reserved. |
ISSN: | 00218693 | DOI: | 10.1016/j.jalgebra.2012.07.043 |
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geprüft am 07.05.2024