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Elimination from Homogeneous Polynomials Over a Polynomial Ring

Published online by Cambridge University Press:  20 November 2018

John G. Stevens*
Affiliation:
Montclair State College, Upper Montclair, New Jersey
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Let Ω be a field and Γ a parameter. We designate the set of all polynomials homogeneous in (X) = (X1, … , Xn) with coefficients in Ω [Γ] by H Ω Γ[X] and write such polynomials as F, F(X), or F(X, Γ). The degree of a polynomial in H Ω Γ [X] shall mean the degree in (X). Let I = (F1 … , Fr) be a fixed ideal in H Ω Γ [X] generated by F1 … , Fr.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Dwork, Bernard, On the zeta function of a hyper surf ace III, Ann. of Math. 83 (I960), 457519.Google Scholar
2. Ehrenpreis, Leon, Fourier analysis in several complex variables (Wiley-Interscience Publishers, New York 1970).Google Scholar
3. Jacobson, Nathan, Lectures in abstract algebra, II, Chap. Ill (D. Van Nostrand Company, Inc., New York 1953).Google Scholar
4. Van, B. L. der Waerden, Modern algebra, II, Chap. XI (Frederick Ungar Publishing Co., New York 1953).Google Scholar