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This paper is concerned with the extent to which the Skolem-Bang
theorems in Diophantine approximations generalize from the
standard setting of $\langle\mathbb{R} , \mathbb{Z}\rangle$ to
structures of the form $\langle F, I \rangle$, where $F$ is an
ordered field and $I$ is an integer part of $F$. We show that some
of these theorems are hold unconditionally in general case
(ordered fields with an integer part). The remainder results are
based on Dirichlet's and Kronecker's theorems. Finally we extend
Dirichlet's theorem: to ordered fields with $IE_{1}$ integer part.
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