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