[GAP Forum] Associative Algebra Element Category

[rcone]

GAP Forum,

Is there is a way to distinguish associative algebra elements from 
non-associative ones?  There does not seem to be a valid category making this 
determination, though I might be missing something! (Please see example 
below).  Nevertheless, I'm guessing there is a way to indirecly do this by 
looking at the parent algebras of elements; similar to finding the parent 
family (group) of a free group element with: FamilyObj(a)!.freeGroup.  Related 
to this, how might one find all the available information via the !. for a 
family?

gap> # Associative algebra example:
gap> A := FreeAssociativeAlgebraWithOne(Rationals,"a","b");
<algebra-with-one over Rationals, with 2 generators>
gap> a := A.a;
(1)*a
gap> b := A.b;
(1)*b
gap> B := FreeAlgebraWithOne(Rationals,"c","d");
<algebra-with-one over Rationals, with 2 generators>
gap> c := B.c;
(1)*c
gap> d := B.d;
(1)*d
gap> ExtRepOfObj(a*(b*a));
[ 0, [ [ 1, 1, 2, 1, 1, 1 ], 1 ] ]
gap> ExtRepOfObj(c*(d*c));
[ 0, [ [ 1, [ 2, 1 ] ], 1 ] ]
gap> IsAssociativeElement(a);
false
gap> IsAssociativeElement(c);
false
gap> CategoriesOfObject(a) = CategoriesOfObject(c);
true

Thanks for the continued help!
Randy Cone