Tópicos de álgebra linear explorados com o auxílio da teoria de Galois

Abstract

Let L=K be a nite Galois extension. In this work, we explore the K-vector space Alt(L) of alternating bilinear forms over L. In particular, we present a decomposition of Alt(L) in direct sum. Also, we study the structure of Alt(L) in the case of cyclic Galois extension L=K. Another aspect of linear algebra that is explored in this dissertation are the K-endomorphisms over L with rank 1, that is, the K-hyperplanes of L.