Komutativni prstenovi i njihovi moduli

master's thesis

• Author: Ivana Gut
• Mentor: Dražen Adamović (mentor)
• Committee member: Dražen Adamović (predsjednik povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Dragutin Svrtan (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu napravljen je pregled osnovnih koncepata komutativnih prstenova i modula. Nakon definicija i osnovnih teorema iz teorije prstenova, u radu se baziramo na komutativne prstenove i definiramo domene glavnih ideala, euklidske domene, domene jedinstvene faktorizacije te dokazujemo teoreme iz tog područja. Poseban naglasak dan je na prstenu polinoma i njegovim svojstvima. Drugi dio rada posvećen je modulima. Osim osnovnih definicija iz teorije modula, obrađujemo i slobodne module.

Abstract (english)

This paper presents an overview of basic concepts concerning commutative rings and modules. Following definitions and basic theorems from ring theory, this paper is focused on commutative rings and definitions of principal ideal domains, Euclidean domains, unique factorization domains completed with proofs of said theorems. A particular emphasis is given to polynomial ring and its attributes. Second part of this paper is dedicated to modules. Apart from basic definitions from module theory, focus is given to free modules.

• Keywords: komutativni prsteni; moduli; teorija prstenova; prsten polinoma; slobodni moduli
• Keywords (english): commutative rings; modules; ring theory; polynomial ring; free modules
• Language: croatian
• URN:NBN: urn:nbn:hr:217:641585
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-29 10:34:02