On linear forms with algebraic coefficients and diophantine equations

In my paper, [Man. Math.18 (1976), Satz 1.1] I proved a result on simultaneous diophantine inequalities for p-adic linear forms with algebraic coefficients. In this paper I shall generalize this result and give a necessary and sufficient criterion for the estimation of a product of complex and p-adic linear forms with algebraic coefficients, implying a theorem of Schmidt, [Math. Ann.191 (1971), Satz 1]. Using this estimate I shall obtain the p-adic generalization of Schmidt's theorems on diophantine equations of norm form type [Ann. of Math.96 (1972)].