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Norms in polynomial rings

Published online by Cambridge University Press:  17 April 2009

G. Myerson
G. Myerson
Affiliation:
Department of Mathematics, Macquarie University, New South Wales 2109, Australia
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We give a formula for the norm on a polynomial ring modulo an ideal in terms of the zero-set of the ideal. We hint at the relation to resultants.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 381 - 386
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Barnett, S., ‘Greatest common divisor of two polynomials’, Linear Algebra Appl. 3 (1970), 7–9.CrossRefGoogle Scholar
[2]Čebotarev, N.G., Teorija Galua (Mathematika w Monografijach, Serija Obsorow I, Moskwa, Leningrad, 1936).Google Scholar
[3]Gröbner, W., Moderne algebraische Geometrie (Springer, Vienna and Innsbruck, 1949).CrossRefGoogle Scholar
[4]Kalman, R.E., ‘Mathematical description of linear dynamical systems’, SIAM J. Control 1 (1963), 152–192.Google Scholar
[5]Lang, S., Algebra (Addison Wesley, Reading, Mass., 1965).Google Scholar
[6]McCoy, N.H., ‘Divisors of zero in matric rings’, Bull.Amer.Math.Soc. 47 (1941), 166–172.CrossRefGoogle Scholar
[7]Myerson, G., ‘On resultants’, Proc. Amer. Math. Soc. 89 (1983), 419–420.CrossRefGoogle Scholar
[8]Netto, E., Vorlesungen über Algebra, vol II (Leipzig, 1900).Google Scholar
[9]Schmidt, H., ‘Bemerkung zur elementaren Algebra: I. Restklassenring und Resultante’, Bayer. Akad. Wiss. Math. – Natur. Kl. Sitzungsber. 1966 II (1967), 167–172.Google Scholar
[10]Vogt, W.G. and Bose, N.K., ‘A method to determine whether two polynomials are relatively prime’, IEEE Trans. Automat. Control AC–15 (1970), 379–380.CrossRefGoogle Scholar