Def A polynomial over a field k (like the rational numbers, real numbers or complex numbers) is called irreducible if it is not a constant and cannot be factored as a product of polynomials (over k) of smaller degree.

More generally, an element of a commutative integral domain R is called irreducible if it is a non-unit and it cannot be written as a product of two non-units in R.

For example, in Z, the ring of integers, the irreducible elements are the prime numbers and their negatives.

If a is irreducible then any associate of a is irreducible. See also prime.