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undergraduate thesis
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Real Fields
Ana Glavačević (2018)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
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Glavačević, A. (2018). Realna polja (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:110142

Glavačević, Ana. "Realna polja." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:110142

Glavačević, Ana. "Realna polja." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:110142

Glavačević, A. (2018). 'Realna polja', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 20 February 2019, https://urn.nsk.hr/urn:nbn:hr:126:110142

Glavačević A. Realna polja [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2019 February 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:110142

A. Glavačević, "Realna polja", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:110142

Metadata
TitleRealna polja
AuthorAna Glavačević
Mentor(s)Ivan Matić (thesis advisor)
Abstract
U ovome radu pisat ćemo o realnim poljima. U uvodnom dijelu navest ćemo definiciju prstena, njegova osnovna svojstva te pojmove poput djelitelj nule, grupa invertibilnih elemenata, polje, proširenje polja, algebarski zatvoreno polje, izomorfizam. Nadalje, u drugom dijelu opisat ćemo uređena polja, prokomentirati postojanje beskonačno velikih brojeva te objasniti arhimedsko polje. Nakon toga ćemo definirati realno polje i iskazati i dokazati bitne teoreme, leme i propozicije vezane uz takvo polje. Također, reći ćemo nešto i o postojanju homomorfizama.
Keywordsan ordering of field ordered field archimedean field valuation ring real field real close field real closure irreducible polynomial Sturm sequence variation of signs in the sequence isomorphism homomorphism
Parallel title (English)Real Fields
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 date2018-09-28
Parallel abstract (English)
In this term paper we write about real fields. In introduction we cite the definition of the ring, it’s elementary characteristics and terms as divisor of zero, integral domain, group of invertible elements, field, extension field, algebraically closed field, isomorphism. Furthermore, in the second part we describe the ordered fields, comment on the existence of infinitely large numbers and explain the archimedean field. After that we define the real field and we state and prove theorems, lemma and propositions related to such a field. We also say something about the existence of homomorphisms
Parallel keywords (Croatian)uređaj na polju uređeno polje arhimedsko polje valuacijski prsten realno polje realno zatvoreno polje realni zatvarač ireducibilan polinom Sturmov niz promjena predznaka u nizu izomorfizam homomorfizam.
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:110142