Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

A simple proof of Zariski's Lemma

Document Type : Research Paper

Author
A. Azarang
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.
Keywords
Zariski's Lemma
PID
Field
Subjects
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.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 5
October 2017
Pages 1529-1530

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