On the Normalization Theorem for Affine Rings and Power Series Rings
Date Issued
2009
Date
2009
Author(s)
Kang, Shih-Cheng
Abstract
In Section 1, we give some applications of the normalization theorem and the geometric significance of the normalization theorem. Moreover, we state all main results among this paper. From Section 2 to Section 5, we discuss the basic normalization theorem and more special versions. In Section 6, we give the classical normalization theorem for power series rings. In Section 7, we give three proofs for Weierstrass Preparation Theorem. One of them is the long division algorithm and the others give us the stronger result. At last, we use the Weierstrass Preparation Theorem to reprove the normalization theorem for power series rings and for convergent power series rings.
Subjects
normalization theorem
normalization lemma
Weierstrass Preparation Theorem
affine ring
power series ring
separable ring
Type
thesis
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