Abel-Ruffinijev teorem

Pavković, Josipa (2016) Abel-Ruffinijev teorem. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

The theme of this diploma thesis is Abel-Ruffini theorem which states that there is no general algebraic solution, that is, solution in radicals, to polynomial equations of degree five or higher. In Chapter 1 we introduce some basic definitions that will be needed to build the foundations of the Galois theory, which we detail in Chapter 4. In Chapter 2 we give a special attention to the ring of polynomials. We are going to see that, when k is a field, virtually all the familiar theorems valid in Z have polynomial analogs in k[x]; moreover, we shall see that the familiar proofs can be generalized. In the third chapter we define quotient ring and introduce the notion of field extension. In Chapter 5 we will briefly show the process of solving equations of the third and fourth degree. In the last chapter we will prove Galois theorem on correspondence between solvability of polynomial in radicals and the corresponding Galois group, and Abel-Ruffini theorem.

Item Type: Thesis (Diploma thesis)
Supervisor: Perše, Ozren
Date: 2016
Number of Pages: 39
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 11 Apr 2016 10:08
Last Modified: 11 Apr 2016 10:08
URI: http://digre.pmf.unizg.hr/id/eprint/4683

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