A simple proof of Zariski's Lemma

Document Type: Research Paper

Author

Department of Mathematics‎, ‎Shahid Chamran University of Ahvaz‎, ‎Ahvaz‎, ‎Iran.

Abstract

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$\mathbb{Q}$ is not a finitely generated $\mathbb{Z}$-algebra.

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References

E. Arrondo, Another elementary proof of the Nullstellensatz, Amer. Math. Monthly 113 (2006), no. 2, 169--171.

K. Hulek, Elementary Algebraic Geometry, Stud. Math. Libr. 20, Amer. Math. Soc. Providence, RI, 2003.

E. Kunz, Introduction to Commutaive Algebra and Algebraic Geometry, Birkhäusher Boston, 1985.

J. McCabe, A Note on Zariski's Lemma, Amer. Math. Monthly 83 (1976), no. 7, 560--561.

M. Reid, Undergraduate Algebraic Geometry, London Math. Soc. Stud. Texts 12, Cambridge Univ. Press, Cambidge, 1988.

History

• Receive Date: 04 July 2016
• Revise Date: 08 August 2016
• Accept Date: 12 August 2016