Dagger closure in regular rings containing a field

Details Dagger closure in regular rings containing a field Dagger closure in regular rings containing a field

2011-03-09

arxiv.org/abs/1103.1786v2

Mathematics

Commutative Algebra

12 pages, added one corollary and two references

Scientific paper

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.

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