2011/03/31 by Holger Brenner, Axel Stäbler
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Closure (psychology) #Combinatorics #Dagger #Discrete mathematics #Field (mathematics) #Law #Mathematical analysis #Mathematics #Polynomial #Polynomial ring #Pure mathematics #Rank (graph theory) #Rings, Modules, and Algebras #math.AC #msc:13A18 #msc:13A35 #msc:13D45
paper · pdf · doi:10.1016/j.jalgebra.2012.07.043
published as J. Algebra 370 (2012), p. 176-185 · 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 exposition
arxiv created 2012/07/03 · openalex publication_date 2012/08/13 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.