On Oct 28, 2006, at 10:05 PM, William Stein wrote:

> Regarding ring and algebra elements, suppose x is in a ring R and y
> is in a K-algebra S.    We want to define what "x * y" means.  The
> most natural thing to me would be
>
>     x * y    is      K._coerce_(x) * y
>
> and that's it.  If no coerce map exists, fail.
>
> Am I missing something?  The above rule is definitely easy to  
> understand.

What if you multiply two CommutativeAlgebraElements? You could either  
attempt the base extension from your previous email, or you could try  
"forgetting" that the guy on the left is a commutative algebra  
element, only treat it as a ringElement, and try the coercion you  
wrote down just above. Could these be different?

David


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