Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T18:22:55.287Z Has data issue: false hasContentIssue false
  • English
  • Français

On Factorization of Polynomials Modulo n

Published online by Cambridge University Press:  20 November 2018

Robert Gilmer
Robert Gilmer*
Affiliation:
Florida State University, Tallahassee Florida
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let A be an ideal of the commutative ring R with identity. There is a canonical homomorphism ϕA from the polynomial ring R[X] onto (R/A)[X], obtained by reducing all coefficients modulo A. If fR[X], then we say that f is reducible (irreducible) modulo A if ϕA(f) is reducible (irreducible) in (R/A)[X].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 521 - 523
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Guerrier, W. J., The factorization of the cyclotomic polynomials modp, Amer. Math. Monthly 75 (1968), p. 46.Google Scholar
2. Jacobson, N., Lectures in abstract algebra, Vol. 3, Van Nostrand, Princeton, N.J., 1964.Google Scholar
3. Redei, L., Algebra, Vol. 1, Pergamon Press, New York, 1967.Google Scholar
4. Ribenboim, P., Théorie des valuations, Univ. of Montreal Press, Montreal, 1964.Google Scholar
5. Snapper, E., Completely primary rings, Ann. of Math. (2) 52 (1950), 666–693.Google Scholar
6. Shanks, D., Solved and unsolved problems in number theory, Spartan Books, Washington, D.C., 1962.Google Scholar
7. van der Waerden, B. L., Algebra, Vol. 2, Ungar, New York, 1970.Google Scholar