F-Pure Homomorphisms, Strong F-regularity, and F-injectivity
F-Pure Homomorphisms, Strong F-regularity, and F-injectivity
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DOI：
10.1080/00927870903431241
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发表时间：
2009-08
影响因子：
0.7
通讯作者：
M. Hashimoto
中科院分区：
文献类型：
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作者：
M. Hashimoto
讨论了强f正则性、f纯度和Cohen-Macaulay f单射性质的Matijevic-Roberts型定理。与此相关，我们还讨论了这些性质的碱基变化问题和位点的开放性问题。特别地，我们用radu - andr<s:1>同态定义了同态的f纯性的概念，并证明了它的基本性质。我们还讨论了强f正则的一个强版本（非常强的f正则），并比较了这两个版本的强f正则。结果表明，强f -正则性和非常强f -正则性在局部环、f -有限环和本质有限型代数上是一致的。证明了强f正则性的f纯碱变化。
We discuss Matijevic–Roberts type theorem on strong F-regularity, F-purity, and Cohen–Macaulay F-injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F-purity of homomorphisms using Radu–André homomorphisms and prove basic properties of it. We also discuss a strong version of strong F-regularity (very strong F-regularity), and compare these two versions of strong F-regularity. As a result, strong F-regularity and very strong F-regularity agree for local rings, F-finite rings, and essentially finite-type algebras over an excellent local rings. We prove the F-pure base change of strong F-regularity.