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The ideal of polynomials vanishing
on a commutative ring


Author: Robert Gilmer
Journal: Proc. Amer. Math. Soc. 127 (1999), 1265-1267
MSC (1991): Primary 13B25; Secondary 13E10
DOI: https://doi.org/10.1090/S0002-9939-99-04634-1
Published electronically: January 27, 1999
MathSciNet review: 1473669
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Abstract | References | Similar Articles | Additional Information

Abstract: We determine equivalent conditions on a commutative Artinian ring $S$ in order that the ideal of $S[t]$ consisting of polynomials that vanish on $S$ should be principal. Our results correct an error in a paper of Niven and Warren.


References [Enhancements On Off] (What's this?)

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  • [N] W. Narkiewicz, Polynomial Mappings, Lecture Notes in Math. 1600 (1995). MR 97e:11037
  • [NW] I. Niven and D. Warren, A generalization of Fermat's Theorem, Proc. Amer. Math. Soc. 8 (1957), 306-313.
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  • [ZS] O. Zariski and P. Samuel, Commutative Algebra, vol. I, Springer, Berlin-Heidelberg, 1986.

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Additional Information

Robert Gilmer
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email: gilmer@math.fsu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04634-1
Keywords: Vanishing polynomials, Artinian rings
Received by editor(s): June 10, 1997
Received by editor(s) in revised form: August 6, 1997
Published electronically: January 27, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society

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