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

Mitsuyasu Hashimoto

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 languageEnglish
Pages (from-to)4569-4596
Number of pages28
JournalCommunications in Algebra
Issue number12
Publication statusPublished - Dec 2010
Externally publishedYes


  • F-Injective
  • F-Pure
  • Strongly F-regular

ASJC Scopus subject areas

  • Algebra and Number Theory


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