 For example, any principal ideal domain "R" is a unique factorization domain (UFD) which means that any element is a product of irreducible elements, in a (up to reordering of factors) unique way.Here, an element "a" in a domain is called irreducible if the only way of expressing it as a product
is by either "b" or "c" being a unit.An example, important in field theory, are irreducible polynomials, i.e., irreducible elements in "k"["X"], for a field "k".