Definition:Irreducible Polynomial

Also see

 * Equivalence of Definitions of Irreducible Polynomial over Field
 * Field is Integral Domain


 * By Units of Ring of Polynomial Forms over Field, a polynomial in a single indeterminate with coefficients in a field is irreducible it is not a product of two polynomial forms of smaller degree.

This is not necessarily true for polynomials over a commutative ring.