 Absolute multiplicative Weil height

For an algebraic number $\alpha$ in a number field $L$, the absolute multiplicative Weil height isIt is independent of the field $L$ containing $\alpha$, satisfies $H({\alpha }^n)=H(\alpha {)}^{|n|}$, and obeys $H(\alpha +\beta )\le 2H(\alpha )H(\beta )$.