The ideal of polynomials vanishing on a commutative ring
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- by Robert Gilmer PDF
- Proc. Amer. Math. Soc. 127 (1999), 1265-1267 Request permission
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
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- Władysław Narkiewicz, Polynomial mappings, Lecture Notes in Mathematics, vol. 1600, Springer-Verlag, Berlin, 1995. MR 1367962, DOI 10.1007/BFb0076894
- I. Niven and D. Warren, A generalization of Fermat’s Theorem, Proc. Amer. Math. Soc. 8 (1957), 306–313.
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- O. Zariski and P. Samuel, Commutative Algebra, vol. I, Springer, Berlin-Heidelberg, 1986.
Additional Information
- Robert Gilmer
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
- Email: gilmer@math.fsu.edu
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1473669