Fungsi Trace dan Fungsi Norm Lapangan Perluasan Atas Q

Abstract

Suppose L/K is an extension field where K⊆L so that L can be viewed as a vector space over K. Moreover, it is known that for every α∈L, we can construct a linear transformation T_α: L→L where T_α (x)=αx for all x∈L so that we have the representation matrix [T_α] of T_α. In this study, the trace and norm functions are discussed which are defined using the trace and determinant of the matrix [T_α]. Furthermore, this study will also discuss the application of the trace and norm functions in the field of an extension field especially Q(∛2) over Q.