Subrings invariant under endomorphisms

Shulim Kaliman

doi:10.1016/S0021-8693(02)00680-4

Subrings invariant under endomorphisms

Shulim Kaliman

Mathematics

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 language	English (US)
Pages (from-to)	31-43
Number of pages	13
Journal	Journal of Algebra
Volume	261
Issue number	1
DOIs	https://doi.org/10.1016/S0021-8693(02)00680-4
State	Published - Mar 1 2003

Fingerprint

ASJC Scopus subject areas

Algebra and Number Theory

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

@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 = mar

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

AN - SCOPUS:0037360046

VL - 261

SP - 31

EP - 43

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -

Access to Document

10.1016/S0021-8693(02)00680-4