Extensões algébricas de corpos: algumas aplicações práticas

Abstract

In this work, our main objective is to present in a simple manner, the process of constructing the root field of a polynomial through the adjunction of roots, where it is a subfield of the complex numbers C. Some cases are explored of rationalization of Elementary Algebra, in simple algebraic extensions of rational numbers, using two distinct methodological approaches obtained from Abstract Algebra. The special case of the nth roots of the polynomial unit is analyzed from a geometric point of view and from the obtainment of its field of roots. Furthermore, a connection between the nth roots of the unit and its application in digital signal processing is presented in a didactic way. Finally, an analysis of a small amplitude vibratory movement is presented, relating it to the roots of a quadratic equation derived from the adopted physical system model.

Keywords: Elementary algebra. Abstract algebra. Algebraic Rationalization.  Signal processing. Stables physical system