Subrings invariant under endomorphisms

Shulim Kaliman

Research output: Contribution to journal › Article

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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Subring
Endomorphisms
Automorphism
Transcendence
Self-intersection
Invariant
Algebraic Variety
Endomorphism
Automorphisms
Ring
Imply

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Subrings invariant under endomorphisms. / Kaliman, Shulim.

In: Journal of Algebra, Vol. 261, No. 1, 01.03.2003, p. 31-43.

Research output: Contribution to journal › Article

Kaliman, S 2003, 'Subrings invariant under endomorphisms', Journal of Algebra, vol. 261, no. 1, pp. 31-43. https://doi.org/10.1016/S0021-8693(02)00680-4
Kaliman S. Subrings invariant under endomorphisms. Journal of Algebra. 2003 Mar 1;261(1):31-43. https://doi.org/10.1016/S0021-8693(02)00680-4
Kaliman, Shulim. / Subrings invariant under endomorphisms. In: Journal of Algebra. 2003 ; Vol. 261, No. 1. pp. 31-43.
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