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Prime element
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{{short description|Analogue of a prime number in a commutative ring}} In [[mathematics]], specifically in [[abstract algebra]], a '''prime element''' of a [[commutative ring]] is an object satisfying certain properties similar to the [[prime number]]s in the [[integer]]s and to [[irreducible polynomial]]s. Care should be taken to distinguish prime elements from [[irreducible element]]s, a concept that is the same in [[unique factorization domain|UFD]]s but not the same in general.
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