Prime element

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Template:Associate-invariant integral domain-element property

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 in an integral domain is said to be prime' if whenever , then or .

Invariance up to associates

Further information: Prime element property is invariant upto associates

Relation with other properties

Weaker properties