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Def/Associate +,
Def/Field +,
Def/Irreducible element +,
Def/Prime element +,
Def/UFD +,
Def/Unique factorization +,
State/Divisibility corresponds to containment of principal ideals +,
State/Fields are integral domains +,
State/Irreducible implies prime in a PID +,
State/No nonzero nilpotents in a field +,
State/Product of units is a unit +
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