nLab content (ring theory)

This entry is about the notion of “content” in ring theory. For the notion in measure theory, see content (measure theory). For the notion in combinatorics/representation theory see hook-content formula. For the contents sidebar of this wiki, see contents. For more disambiguation see content.

Definition

Let $R$ be a unique factorization domain with decidable equality. The content of a polynomial $p \in R[x]$ is the greatest common divisor of the coefficients

$$\gcd_{i \leq d(p)} p_i$$

where $d(p)$ is the degree of the polynomial.

See also

• polynomial

• Gauss's lemma for polynomials?

• rational root theorem

References

• Wikipedia, Primitive part and content