over a field k
s, real number
s or complex number
s) is called
if it is not a constant
and cannot be factor
ed 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.