Moduli nad domenama glavnih ideala

master's thesis

• Author: Dora Hrvoj
• Mentor: Ozren Perše (mentor)
• Committee member: Ozren Perše (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-02-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Glavni cilj ovog rada je proučiti pojam $R$-modula gdje je $R$ domena glavnih ideala. Rad se sastoji od dvaju poglavlja. U prvom poglavlju predstavljaju se osnovne algebarske strukture, grupe i prstenovi te se pojašnjavaju moduli. U drugom poglavlju detaljnije se predstavljaju moduli nad domenama glavnih ideala. U ovom radu, glavni naglasak stavljen je na konačno generirane module čiji rezultati proizlaze iz generaliziranih tvrdnji o Abelovim grupama. Strukturne teoreme za konačne Abelove... More grupe generalizirat ćemo na module nad domenama glavnih ideala, iz čega zaključujemo da se ne generaliziraju samo teoremi već i dokazi. Less

Abstract (english)

The main objective of this paper is to study the notion of $R$-module where $R$ is the principal ideal domain. This paper consists of two chapters, the first chapter presenting basic algebraic structures, groups and rings and explaining the modules. The second chapter presents the modules over principal ideal domain in more detail. The main emphasis of this paper is placed on the finitely generated modules whose results are derived from generalized statements about Abelian groups. We... More will generalize the structural theorems for finite Abelian groups to modules over principal ideal domain, from which we conclude that not only the theorems are generalized but also the proofs. Less

• Keywords: algebarske strukture; grupe; prstenovi; moduli; Abelove grupe
• Keywords (english): algebraic structures; groups; rings; modules; Abelian groups
• Language: croatian
• URN:NBN: urn:nbn:hr:217:130169
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-07-23 10:44:58