Construction of strictly closed rings

Abstract

The notion of strict closedness of rings was given by J. Lipman in connection with a conjecture of O. Zariski. The present purpose is to give a practical method of construction of strictly closed rings. It is also shown that the Stanley-Reisner rings of simplicial complexes (resp. $F$-pure rings satisfying the condition $(S_2)$ of Serre) are strictly closed (resp. weakly Arf) rings.

11 pages. The title was changed from Weakly Arf rings and Frobenius actions. We also added Section 2

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• Excellence, F-singularities, and solidity