Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Noether Normalization Implies Full Form of Hilbert Nullstellensatz Theorem

  • Alborz Azarang (Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz)
  • Received : 2022.02.24
  • Accepted : 2022.07.25
  • Published : 2023.03.31
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Abstract

We give a new proof for the full form of Hilbert's Nullstellensatz based on on integral extension and Noether's Normalization Lemma.

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Acknowledgement

This work was supported by Research Council of Shahid Chamran University of Ahvaz (Ahvaz-Iran) Grant Number: SCU.MM1400.721.

References

  1. A. Azarang,A simple proof of Zariski's lemma, Bull. Iranian Math. Soc., 43(5)(2017), 1529-1530. 
  2. P. M. Cohn, Basic Algebra: Groups, Rings and Fields, Springer-Verlag London, London(2003). 
  3. J. A. Eagon, Finitely generated domain over Jacobson semisimple rings are Jacobson semisimple, Amer. Math. Monthly, 74(1967) 1091-1092.  https://doi.org/10.2307/2313619
  4. D. Eisenbud, Commutative Algebra: With a View Toward Algebraic Geometry, Graduate Texts in Mathematics, Springer-Verlag, New York(1995). 
  5. R. Gilmer,Multiplicative Ideal Theory, Pure and Applied Mathematics, Marcel-Dekker, New York(1972). 
  6. I. Kaplansky, Commutative Rings, The University of Chicago Press, Chicago(1974). 
  7. R. Y. Sharp, Steps in Commutative Algebra, London Mathemathecal Society Student Texts, Camberidge University Press, Camberidge(2000).