# Infinite dimensional finitely generated algebraic division algebra

Is there a division algebra $$D$$ with center $$K$$ that satisfies the following 3 conditions?

1) $$D$$ is of infinite dimension over $$K$$;

2) every element of $$D$$ is algebraic over $$K$$;

3) $$D$$ is finitely generated (as division $$K$$-algebra).