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.