Hey Joseph,
   It is basically just Parent. I don't know of any other ABC that is a 
subclass of Parent. Although a common concrete implementation of Parent 
that is often used as a base class (for algebras) is 
CombinatorialFreeModule.

Best,
Travis

PS - a more up-to-date version is 
http://doc.sagemath.org/html/en/reference/structure/sage/structure/element.html.

On Thursday, August 4, 2016 at 6:57:49 PM UTC-5, Joseph Hundley wrote:
>
> Is there some analogue of 
>
> http://combinat.sagemath.org/doc/reference/structure/sage/structure/element.html#
> for parent structures? 
>

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