### Abstract

Let p be a prime number. We define the notion of F-finiteness of homomorphisms of F_{p}-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on F-finiteness of homomorphisms of F_{p}-algebras. As a corollary, we prove the following. Let g: B C be a homomorphism of Noetherian F_{p}-algebras. If g is faithfully flat reduced and C is F-finite, then B is F-finite. This is a generalization of Seydi’s result on excellent local rings of characteristic p.

Original language | English |
---|---|

Pages (from-to) | 205-213 |

Number of pages | 9 |

Journal | Osaka Journal of Mathematics |

Volume | 52 |

Issue number | 1 |

Publication status | Published - Jan 1 2015 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'F-finiteness of homomorphisms and its descent'. Together they form a unique fingerprint.

## Cite this

Hashimoto, M. (2015). F-finiteness of homomorphisms and its descent.

*Osaka Journal of Mathematics*,*52*(1), 205-213.