Editing Prime element (section)

==Examples==
The following are examples of prime elements in rings:
* The integers {{math|±2}}, {{math|±3}}, {{math|±5}}, {{math|±7}}, {{math|±11}}, ... in the [[ring of integers]] {{math|'''Z'''}}
* the complex numbers {{math|(1 + ''i'')}}, {{math|19}}, and {{math|(2 + 3''i'')}} in the ring of [[Gaussian integers]] {{math|'''Z'''[''i'']}}
* the polynomials {{math|''x''<sup>2</sup> − 2}} and {{math|''x''<sup>2</sup> + 1}} in {{math|'''Z'''[''x'']}}, the [[ring of polynomials]] over {{math|'''Z'''}}.
* 2 in the [[quotient ring]] {{math|'''Z'''/6'''Z'''}}
* {{math|''x''<sup>2</sup> + (''x''<sup>2</sup> + ''x'')}} is prime but not irreducible in the ring {{math|'''Q'''[''x'']/(''x''<sup>2</sup> + ''x'')}}
* In the ring {{math|'''Z'''<sup>2</sup>}} of pairs of integers, {{math|(1, 0)}} is prime but not irreducible (one has {{math|1=(1, 0)<sup>2</sup> = (1, 0)}}).
* In the [[ring of algebraic integers]] <math>\mathbf Z[\sqrt{-5}],</math> the element {{math|3}} is irreducible but not prime (as 3 divides <math>9=(2+\sqrt{-5})(2-\sqrt{-5})</math> and 3 does not divide any factor on the right).