Prime element: Difference between revisions
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{{integral domain-element property}} | {{associate-invariant integral domain-element property}} | ||
==Definition== | ==Definition== | ||
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A nonzero element <math>p</math> in an integral domain is said to be ''prime''' if whenever <math>p|ab</math>, then <math>p|a</math> or <math>p|b</math>. | A nonzero element <math>p</math> in an integral domain is said to be ''prime''' if whenever <math>p|ab</math>, then <math>p|a</math> or <math>p|b</math>. | ||
===Invariance up to associates=== | |||
{{further|[[Prime element property is invariant upto associates]]}} | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 22:29, 31 January 2009
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