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undergraduate thesis
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Gaussian Integers
Ines Petrić (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Metadata
TitleGaussovi cijeli brojevi
AuthorInes Petrić
Mentor(s)Mirela Jukić Bokun (thesis advisor)
Abstract
U ovom radu bavit ćemo se Gaussovim cijelim brojevima. Reći ćemo nešto općenito o tom skupu, definirat ćemo normu i navesti invertibilne elemente. Takoder ćemo reći nešto o djeljivosti u skupu Gaussovih cijelih brojeva gdje ćemo iskazat važan Teorem o dijeljenju s ostatkom, Euklidov algoritam i Bezoutov teorem. Na kraju ćemo se upoznati s faktorizacijom Gaussovih cijelih brojeva i vidjeti njihovu primjenu.
Keywordsnorm invertible elements divisibility the Division theorem the Euclidean algorithm relatively prime the Gaussian integers composite and prime the Gaussian integers unique factorization
Parallel title (English)Gaussian Integers
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Algebra and Calculus Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Algebra
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2016-09-28
Parallel abstract (English)
In this article we will cover the Gaussian integers. We will say something in general about this set, define the norm and specify invertible elements. Also, we will say something about divisibility in Z[i] where we will demonstrate an important the Divison theorem, Euclidean algorithm and Bezout’s theorem. We will get acquainted with the factorization of Gaussian integers and see some of their application.
Parallel keywords (Croatian)norma invertibilni elementi djeljivost Teorem o dijeljenju s ostatkom Euklidov algoritam relativno prosti Gaussovi cijeli brojevi sloˇzeni i prosti Gaussovi cijeli brojevi jedinstvena faktorizacija
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:587525