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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Originally Posted by Aki 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. For (1), notice that a variable change is an automorphism of your ring. This means that it has an inverse... For (2), assume then look at the ideal generated by & .
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