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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A product formula for minimal polynomials and degree bounds for inverses of polynomial automorphisms


Author: Jie Tai Yu
Journal: Proc. Amer. Math. Soc. 123 (1995), 343-349
MSC: Primary 12E05; Secondary 12F05, 12Y05
MathSciNet review: 1216829
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Abstract: By means of Galois theory, we give a product formula for the minimal polynomial G of $ \{ {f_0},{f_1}, \ldots ,{f_n}\} \subset K[{x_1}, \ldots ,{x_n}]$ which contains n algebraically independent elements, where K is a field of characteristic zero. As an application of the product formula, we give a simple proof of Gabber's degree bound inequality for the inverse of a polynomial automorphism.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1216829-4
PII: S 0002-9939(1995)1216829-4
Keywords: Minimal polynomials, Galois theory, product formula, polynomial automorphisms
Article copyright: © Copyright 1995 American Mathematical Society