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master's thesis
Multilinearna preslikavanja i tenzorski produkt
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:768346
Knežević, Dragana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Knežević, D. (2016). Multilinearna preslikavanja i tenzorski produkt (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:768346

Knežević, Dragana. "Multilinearna preslikavanja i tenzorski produkt." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:768346

Knežević, Dragana. "Multilinearna preslikavanja i tenzorski produkt." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:768346

Knežević, D. (2016). 'Multilinearna preslikavanja i tenzorski produkt', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:768346

Knežević D. Multilinearna preslikavanja i tenzorski produkt [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:768346

D. Knežević, "Multilinearna preslikavanja i tenzorski produkt", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:768346

Metadata
TitleMultilinearna preslikavanja i tenzorski produkt
AuthorDragana Knežević
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu, glavni cilj nam je proučiti pojam tenzorskog produkta modula nad komutativnim prstenom. Rad se sastoji od dva poglavlja. U prvom poglavlju upoznajemo osnovne algebarske strukture koje su nam bile potrebne u daljnjim razmatranjima. Upoznajemo grupe, prstene i ideale, te nešto više pažnje posvećujemo modulima koji su nam bili vrlo bitni u drugom dijelu ovog rada. Također definiramo preslikavanja između navedenih algebarskih struktura. U drugom poglavlju su nam bila važna multilinearna preslikavanja modula da bi mogli definirati pojam tenzorskog produkta. U drugom se poglavlju, dakle, prvo upoznajemo s multilinearnim preslikavanjima, a zatim sa tenzorskim produktom. Osim nekih osnovnih svojstava tenzorskog produkta definirali smo i ravne module i upoznali neka njihova svojstva. Pokazali smo i kako se osnovni prsten može proširiti. Pokazali smo i kako konstruirati tenzorski produkt algebri. Na kraju smo se upoznali sa još dva bitna pojma, tenzorskom algebrom i simetričnom algebrom.
Abstract (english)
The main goal of this diploma thesis is to study the concept of tensor product of modules over commutative ring. The thesis consists of two major parts. The first part explains the basic algebraic structures that will be required for further considerations. We describe groups, rings and ideals, and some attention is paid to the modules that have been very important in the second part of this work. We will define maps between the algebraic structures above as well. In the second part we will be focused on a multilinear maps to be able to define the notion of tensor product. In addition to some basic properties of tensor product, we also define flat modules and study some of their properties. We have shown how the basic ring can be extended. We have also constructed the tensor product of algebras. And finally, we introduced two very important notions, tensor algebra and symmetric algebra.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:768346
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-13 11:42:14