### Ideals in the Group Algebra C[GL(2,R)]

I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.

```
sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False
```

I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.

```
sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True
```

I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!