Non-zero values of linear forms in logarithms

The main objective of the research is a generalization of the result of Stewart and Yu on the abc conjecture, the one giving a non-trivial upper bound \max(|a|,|b|,|c|)\ll\exp(\rad(abc)^{1/3+\varepsilon}), for any $\varepsilon>0$ and integers a, b anc c satisfying a+b=c. The main aim is to extend this result from integers to algebraic integers, in which case a generalization of the abc conjecture has been set up, for example, by Masser [D.W. Masser, ``On abc and discriminants'', Proceedings of the AMS, Vol. 130, Number 11, pp. 3141--3150].
Such a result, clearly, would be interesting on its own (it seems that at present there are no non-trivial results in this direction available for algebraic integers). Also, such a result would have had some potential applications on the effective Skolem-Mahler-Lech problem.