Irreducible element

Definition

A nonzero element in an integral domain is said to be irreducible if it is neither zero nor a unit, and it cannot be expressed as the product of two elements, neither of which is a unit.

Relation with other properties

Stronger properties

• Prime element: For proof of the implication, refer Prime element implies irreducible and for proof of its strictness (i.e. the reverse implication being false) refer Irreducible element not implies prime
• Universal side divisor: For proof of the implication, refer Universal side divisor implies irreducible and for proof of its strictness (i.e. the reverse implication being false) refer Irreducible not implies universal side divisor