Editing Polynomial ring (section)

====Polynomial decomposition====
{{main|Polynomial decomposition}}

A ''decomposition'' of a polynomial is a way of expressing it as a [[function composition|composition]] of other polynomials of degree larger than 1. A polynomial that cannot be decomposed is ''indecomposable''. [[Ritt's polynomial decomposition theorem]] asserts that if <math>f = g_1 \circ g_2 \circ \cdots \circ g_m = h_1 \circ h_2 \circ \cdots\circ h_n</math> are two different decompositions of the polynomial <math>f</math>, then <math>m = n</math> and the degrees of the indecomposables in one decomposition are the same as the degrees of the indecomposables in the other decomposition (though not necessarily in the same order).