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Primitive polynomial

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A polynomial , where is a unique factorization domain, whose coefficients do not have common factors. Any polynomial can be written in the form with a primitive polynomial and the greatest common divisor of the coefficients of . The element , defined up to multiplication by invertible elements of , is called the content of the polynomial . Gauss' lemma holds: If , then . In particular, a product of primitive polynomials is a primitive polynomial.

References

[1] O. Zariski, P. Samuel, "Commutative algebra" , 1 , Springer (1975)


Comments

References

[a1] P.M. Cohn, "Algebra" , 1 , Wiley (1982) pp. 165
[a2] G. Birkhoff, S. MacLane, "A survey of modern algebra" , Macmillan (1953) pp. 79
How to Cite This Entry:
Primitive polynomial. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Primitive_polynomial&oldid=34239
This article was adapted from an original article by L.V. Kuz'min (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article