F-Pure Homomorphisms, Strong F-regularity, and F-injectivity

Mitsuyasu Hashimoto

doi:10.1080/00927870903431241

F-Pure Homomorphisms, Strong F-regularity, and F-injectivity

Mitsuyasu Hashimoto

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	4569-4596
Number of pages	28
Journal	Communications in Algebra
Volume	38
Issue number	12
DOIs	https://doi.org/10.1080/00927870903431241
Publication status	Published - Dec 2010

Keywords

F-Injective
F-Pure
Strongly F-regular

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870903431241

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AB - 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.

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F-Pure Homomorphisms, Strong F-regularity, and F-injectivity

Abstract

Keywords

ASJC Scopus subject areas

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