When is the strict closure of rings finitely generated?

Abstract

This paper investigates the finite generation of the strict closure of rings in arbitrary dimension. For a Noetherian local ring $(R,\mathfrak{m})$, we provide a sufficient condition under which the strict closure $R^{\ast }$ is finitely generated as an $R$-module. Using this result, we characterize the finite generation of the strict closure over excellent rings.

arXiv commentPreprint version, 4 pages. The final authenticated version is to appear in Archiv der Mathematik