Invarijante konačnih grupa na algebri polinoma

master's thesis

• Author: Kristina Nikičić
• Mentor: Goran Muić (mentor)
• Committee member: Goran Muić (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome radu proučavamo invarijante konačnih matričnih grupa. Kao najosnovniji primjer takvih invarijanti javljaju se simetrični polinomi u \(n\) varijabli s koeficijentima iz proizvoljnog polja \(k\). Upravo te simetrične polinome detaljno proučavamo, a dokazujemo i Fundamentalni teorem za simetrične polinome. Pristup proučavanju ovih tema jest elementaran i ni na koji način potpun.

Abstract (english)

In this thesis, we study invariants of a finite matrix groups. The most basic example of such invariants is given by symmetric polynomials in \(n\) variables with coefficients in arbitrary field \(k\). Furthermore, we prove The fundamental theorem of symmetric polynomials. Our treatment is elementary and by no means complete.

• Keywords: konačne matrične grupe; simetrični polinomi; Fundamentalni teorem za simetrične polinome
• Keywords (english): finite matrix groups; symmetric polynomials; fundamental theorem of symmetric polynomials
• Language: croatian
• URN:NBN: urn:nbn:hr:217:006334
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-06-10 10:41:06