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 it satisfies the following equivalent conditions:

Definition with symbols

A nonzero element p in an integral domain R is said to be prime' if it satisfies the following:

Invariance up to associates

Further information: Prime element property is invariant upto associates

Given two associate elements, one of them is prime if and only if the other one is.

Relation with other properties

Weaker properties