On maximal and minimal linear matching property

Abstract

The matching basis in field extentions is introduced by S. Eliahou and C. Lecouvey in [2]. In this paper we define the minimal and maximal linear matching property for field extensions and prove that if \(K\) is not algebraically closed, then \(K\) has minimal linear matching property. In this paper we will prove that algebraic number fields have maximal linear matching property. We also give a shorter proof of a result established in [6] on the fundamental theorem of algebra.