Integral domain in which every irreducible is prime
This article defines a property of integral domains, viz., a property that, given any integral domain, is either true or false for that.
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VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions
Definition
An integral domain in which every irreducible is prime is an integral domain satisfying the following equivalent condition: every irreducible element in it is a prime element.