### 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 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

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

**Subrings invariant under endomorphisms.** / Kaliman, Shulim.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 261, no. 1, pp. 31-43. https://doi.org/10.1016/S0021-8693(02)00680-4

}

TY - JOUR

T1 - Subrings invariant under endomorphisms

AU - Kaliman, Shulim

PY - 2003/3/1

Y1 - 2003/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037360046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037360046&partnerID=8YFLogxK

U2 - 10.1016/S0021-8693(02)00680-4

DO - 10.1016/S0021-8693(02)00680-4

M3 - Article

VL - 261

SP - 31

EP - 43

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -