# possible bug: kernel of ring homomorphism

The kernel of a ring homomorphism to a quotient ring gives unexpected results:

```
A.<t> = QQ[]
B.<x,y> = QQ[]
H = B.quotient(B.ideal([B.1]))
f = A.hom([H.0], H)
f
f.kernel()
```

outputs:

```
Ring morphism:
From: Univariate Polynomial Ring in t over Rational Field
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (y)
Defn: t |--> xbar
Principal ideal (t) of Univariate Polynomial Ring in t over Rational Field
```

whereas the kernel of f:A[t]->B[x,y]->B[x,y]/(y), for f(t)=x should be (0).

Why?

Also discussed on sage-devel.

Now reported on trac.