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Dagger closure in regular rings containing a field

By Holger Brenner and Axel Stäbler


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.Comment: 12 pages, v2: added one corollary and two references, v3: Major simplification in proof of main thm due to the suggestion of a referee, minor changes in expositio

Topics: Mathematics - Commutative Algebra, 13A35, 13A18 (Primary) 13D45 (Secondary)
Year: 2012
DOI identifier: 10.1016/j.jalgebra.2012.07.043
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