Re: polynomial algebra question

From: John H Palmieri <palmieri@xxxxxxxxxxxxxxxxxxx>
Date: Tue, 19 Apr 2005 16:28:05 -0700

On Apr 19 2005, "Chip Eastham" <hardmath@xxxxxxxxx> wrote:

> John H Palmieri wrote:
>> Suppose K/F is a field extension, A is a commutative F-algebra, and
>> (K tensor_F A) is isomorphic to K[x]. Must A be isomorphic to F[x]?
>>
>> I know that the answer is yes with some added hypotheses, but I'm
>> wondering if it's true without them.
>
> Hi, John:
>
> Do we not need to specify the sense in which (K tensor_F A) is
> isomorphic to K[x}?
>
> Surely an isomorphism as F-modules (vector spaces) is too little, as
> this can only guarantee equality of dimensions.
>
> regards, chip

Isomorphic as K-algebras.

--
J. H. Palmieri
Associate Professor of Mathematics University of Washington
Box 354350, Seattle, WA 98195-4350 palmieri@xxxxxxxxxxxxxxxxxxx
http://www.math.washington.edu/~palmieri/
.

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