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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