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I assume f is a and g is x*y - z?

If so, maybe this does what you want?

sage: R.<x, y, z> = QQ['x, y, z']

sage: f = x^2*y - x - z
sage: g = x*y - z

sage: J = R.ideal(g)
sage: r = J.reduce(f)
sage: r
x*z - x - z