Subrings invariant under endomorphisms

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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 languageEnglish (US)
Pages (from-to)31-43
Number of pages13
JournalJournal of Algebra
Volume261
Issue number1
DOIs
StatePublished - Mar 1 2003

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ASJC Scopus subject areas

  • Algebra and Number Theory

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