Is the following statement true ? If so, how is it proven ?

(1) Let

is irreducible, where is a field.

Then it is still irreducible after any variable change

(2) is not a principal ideal domain,

when .

Thank you in advance.

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- Jun 4th 2010, 04:41 AMAkiirreducible polynomial
Is the following statement true ? If so, how is it proven ?

(1) Let

is irreducible, where is a field.

Then it is still irreducible after any variable change

(2) is not a principal ideal domain,

when .

Thank you in advance. - Jun 4th 2010, 05:40 AMSwlabr