### Abstract

Let S and R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0, R be embedded as a subring in S, and F: S → S be an endomorphism such that F(R) ⊂ R. Suppose that every ideal of height 1 in R generates a proper ideal in S, and the spectrum of R has no self-intersection points. We show that if F is an automorphism so is F _{R} : R → R. When R and S have the same transcendence degree then the fact that F _{R} is an automorphisms implies that F is an automorphism.

Original language | English (US) |
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Pages (from-to) | 31-43 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 261 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2003 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Kaliman, S. (2003). Subrings invariant under endomorphisms.

*Journal of Algebra*,*261*(1), 31-43. https://doi.org/10.1016/S0021-8693(02)00680-4