If you ask for operator.mul instead of operator.div then you get the
poly ring.  Is that it, perhaps?

John

On 5 February 2015 at 18:48, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
> sage: cm = sage.structure.element.get_coercion_model()
> sage: cm.explain(GF(5)['x'], ZZ, operator.div)
> Coercion on right operand via
>     Composite map:
>       From: Integer Ring
>       To:   Univariate Polynomial Ring in x over Finite Field of size 5
>       Defn:   Natural morphism:
>               From: Integer Ring
>               To:   Finite Field of size 5
>             then
>               Polynomial base injection morphism:
>               From: Finite Field of size 5
>               To:   Univariate Polynomial Ring in x over Finite Field of size 
> 5
> Arithmetic performed after coercions.
> Result lives in Fraction Field of Univariate Polynomial Ring in x over
> Finite Field of size 5
> Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
>
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