In abstract algebra, a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units.
Contents
Relationship with prime elements
Irreducible elements should not be confused with prime elements. (A non-zero non-unit element
Moreover, while an ideal generated by a prime element is a prime ideal, it is not true in general that an ideal generated by an irreducible element is an irreducible ideal. However, if
Example
In the quadratic integer ring
but