Kyungpook Mathematical Journal 2023; 63(1): 11-13
Published online March 31, 2023
Copyright © Kyungpook Mathematical Journal.
Noether Normalization Implies Full Form of Hilbert Nullstellensatz Theorem
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz-Iran
e-mail : firstname.lastname@example.org
Received: February 24, 2022; Accepted: July 25, 2022
We give a new proof for the full form of Hilbert’s Nullstellensatz based on on integral extension and Noether’s Normalization Lemma.
Keywords: Field, Noether Normalization
Recall the statements of the the weak and strong forms Hilberts's Nullstellensatz and of Noether's Nomalisation Lemma.
Theorem 1.1. (Hilbert's Nullstellensatz (weak form) Let
Theorem 1.2. (Hilbert's Nullstellensatz (full form) Let
Theorem 1.3. (Noether's Normalization Lemma) Let
Usually, the weak form of Hilbert's Nullstellensatz is proved by some technical and classical facts such as Noether's Normalization Lemma, Zariski's Lemma, Artin-Tate Lemma and the concept of
In this short note we prove that Noether's Normalization Lemma also implies the full form of Hilbert's Nullstellensatz Theorem.
Let us recall some standard definitions and facts from commutative ring theory which will be used in this note. For a ring
This work was supported by Research Council of Shahid Chamran University of Ahvaz (Ahvaz-Iran) Grant Number: SCU.MM1400.721.
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