Content deleted Content added
Line 13:
<math>R = \frac{\mathbb{F}_q[x]}{\langle f(x) \rangle}</math>. If we suppose that <math>f(x)</math> has irreducible factors <math>p_1(x), p_2(x), \ldots, p_s(x)</math>, all of degree ''d'', then this factor ring is isomorphic to the [[direct product]] of factor rings <math>S = \prod_{i=1}^s \frac{\mathbb{F}_q[x]}{\langle p_i(x) \rangle}</math>. The isomorphism from ''R'' to ''S'', say <math>\phi</math>, maps a polynomial <math>g(x) \in R</math> to the ''s''-tuple of its reductions modulo each of the <math>p_i(x)</math>, i.e. if:
\begin{align}
g(x) & {} \equiv g_1(x) \pmod{p_1(x)}, \\
| |||