Creating ideals of finitely presented algebras in MAGMA

Question

I want to create (right, left, two-sided) ideals of a finitely-presented algebra in MAGMA. I know how to do this for a free algebra, and the magma handbook indicates that it's possible to do this for finitely-presented algebras too. However, when I run the following code,

K := RationalField();
F<z> := FreeAlgebra(K,1);
A<z> := quo<F|z^3>;

I := ideal<F|z^2>;

I get the error Runtime error in ideal< ... >: Rhs argument 1 is invalid for this constructor. Is it actually possible to do this?

Answer 1

The problem is you are redefining $z$ to be the variable of $A$, and it is then no longer recognized as an element of $F$. Try this

K := RationalField();
F<x> := FreeAlgebra(K,1);
A<z> := quo<F|x^3>;

I := ideal<F|x^2>;

Now Magma knows that when you refer to $x$, you are talking about the variable of $F$ and when you talk about $z$, you are talking about the variable of $A$.