F-coherent rings with applications to tight closure theory
F-coherent rings with applications to tight closure theory
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DOI：
10.1016/j.jalgebra.2011.05.006
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
Kazuma Shimomoto
中科院分区：
文献类型：
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作者：
Kazuma Shimomoto
本文的目的是引入一类新的通过完全闭包刻画素特征的Noether环，并研究它们的基本性质。如果Noether环的完美闭包是凝聚的，我们称之为F-凝聚环。给出了紧闭包理论的一些应用。特别地，我们讨论了F-凝聚环与F-纯环、F-正则环和F-内射环之间的一些关系。作为主要工具，我们使用估值理论中的技术。最后一节讨论了凝聚性如何影响一般完全环上生成理想的紧闭性。
The aim of this paper is to introduce a new class of Noetherian rings of prime characteristic via perfect closure and study their basic properties. If the perfect closure of a Noetherian ring is coherent, we call it anF-coherent ring. Some applications are given to tight closure theory. In particular, we discuss some relationship betweenF-coherent rings andF-pure,F-regular, andF-injective rings. As a main tool, we use techniques from valuation theory. The final section discusses how the coherent property effects the behavior of tight closure of finitely generated ideals on general perfect rings.