Construction of strictly closed rings

Construction of strictly closed rings

The notion of strict closedness of rings was given by J. Lipman [Amer. J. Math. 93 (1971), pp. 649–685] 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 simpli...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2022-01, Vol.150 (1), p.119-129
Hauptverfasser: Endo, Naoki, Goto, Shiro
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description The notion of strict closedness of rings was given by J. Lipman [Amer. J. Math. 93 (1971), pp. 649–685] 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 (\operatorname {S}_2) of Serre) are strictly closed (resp. weakly Arf) rings.
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