Subrings invariant under endomorphisms

Research output: Contribution to journalArticle

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

Fingerprint

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 journalArticle

@article{8f7f1cf7b07d428fa061f4addb662a7d,
title = "Subrings invariant under endomorphisms",
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.",
author = "Shulim Kaliman",
year = "2003",
month = "3",
day = "1",
doi = "10.1016/S0021-8693(02)00680-4",
language = "English (US)",
volume = "261",
pages = "31--43",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "1",

}

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 -