The Skolem–Bang theorems in ordered fields with an IP

This paper is concerned with the extent to which the Skolem–Bang theorems in Diophantine approximations generalize from the standard setting of to structures of the form F,I , 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 Dirichletʹs and Kroneckerʹs theorems. Finally we extend Dirichletʹs theorem to ordered fields with IE1 integer part.