View source for Primitive polynomial

A [[Polynomial|polynomial]] $f(X) \in R[X]$, where $R$ is a unique factorization domain, whose coefficients do not have common factors. Any polynomial $g(X) \in R[X]$ can be written in the form $g(X) = c(g) f(X)$ with $f(X)$ a primitive polynomial and $c(g)$ the [[greatest common divisor]] of the coefficients of $g(X)$. The element $c(G) \in R$, defined up to multiplication by invertible elements of $R$, is called the content of the polynomial $g(X)$. Gauss' lemma holds: If $g_1(X), g_2(X) \in R[X]$, then $c(g_1g_2) = c(g_1)c(g_2)$. In particular, a product of primitive polynomials is a primitive polynomial.

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  O. Zariski,   P. Samuel,   "Commutative algebra" , '''1''' , Springer  (1975)</TD></TR>
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====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  P.M. Cohn,   "Algebra" , '''1''' , Wiley  (1982)  pp. 165</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  G. Birkhoff,   S. MacLane,   "A survey of modern algebra" , Macmillan  (1953)  pp. 79</TD></TR>
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