Matrice nad nekomutativnim prstenima

Fijan, Lucija (2016) Matrice nad nekomutativnim prstenima. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

The theme of this paper are matrices over noncommutative ring. In the first and second chapter titled Rings and Modules we introduce the basic concepts that are required in the far part of the work. The concept semisimplicity, the main theme of the third chapter, is the most basic term that runs through this entire graduate paper. We present three definitions of semisimple modules and prove that they are equivalent. Besides Jacobson’s theorem we also prove some others very important theorems, for example Wedderbun’s theorem which gives us a representation of a ring R as the ring of D-endomorphisms of module E, where D is a finite-dimensional division algebra over a field k. Using the above conditions we can prove Jacobson’s density theorem and define the terms of semisimple and simple ring.

Item Type: Thesis (Diploma thesis)
Supervisor: Perše, Ozren
Date: 2016
Number of Pages: 27
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 20 Oct 2016 09:25
Last Modified: 20 Oct 2016 09:25
URI: http://digre.pmf.unizg.hr/id/eprint/5188

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