Prime element

Definition

Symbol-free definition

A nonzero element in an integral domain is said to be a prime element if whenever it divides the product of two elements, it must divide at least one of them.

Definition with symbols

A nonzero element $p$ in an integral domain is said to be prime' if whenever $p|ab$, then $p|a$ or $p|b$.

Relation with other properties

Weaker properties

• Irreducible element