Algebraliste võrrandite lahenduvus radikaalides

Abstract

In the thesis we studied the problem of solving the algebraic equations by radicals { a problem which has interested mathematicians for centuries. In particular we studied the group theory and the eld theory which helped us to research into the matter of solving the algebraic equations by radicals. We then learned about Lagrange's idea of solving the equations of lower degree which served as a starting point for developing Galois theory. Using the latter, we were nally able to provide a criterion for solving the equations by radicals. By using that criterion we showed that not all equations of fth degree can be solved by radicals. It became evident that in order to prove the fact a lot of work had to be done. Nevertheless, the original ideas from Lagrange and Galois are worth investigating. We just have to agree with the words of Professor Gunnar Kangro (see [1], page 154): The research made by Galois presents one of the deepest and most fruitful theories, ever done by the spirit of man. Galois theory has been investigated further nowadays and there is an abstract theory for solving the equations by radicals. Current studying material is a good starting point for anyone who is interested in this theory.