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) |
|---|---|
| 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