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 ...

We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain ...

The objective of this paper is to present the Inverse Problem of Galois, which is to discover under what conditions we can determine a polynomial that has G as a Galois group. Therefore, the Galois Theory is addressed, if ...

We will give three characterizations of such fields and an application to quadratic forms in characteristic 2.

The objective of this text is to give a brief introduction to Galois theory and to computer the Galois groups of low degree polynomials in a field of caracteristic zero.

Strong similarities have been long observed between the Galois (Categories Galoisiennes) and the Tannaka (Categories Tannakiennes) theories of representation of groups. In this paper we construct an explicit (neutral) ...

Solving polynomial equations was a problem that followed countless mathematicians over the centuries. As mathematics improved, formulas for Ąnding polynomial roots were developed. But the great mystery that plagued the ...