| Title | Realna polja |
| Author | Ana 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. |
| Keywords | an 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 |
| Granter | Josip Juraj Strossmayer University of Osijek
Department of Mathematics |
| Lower level organizational units | Chair of Pure Mathematics
Algebra and Calculus Research Group |
| Place | Osijek |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
Algebra
|
| Study programme type | university |
| Study level | undergraduate |
| Study programme | University undergraduate study programme in mathematics |
| Academic title abbreviation | univ.bacc.math. |
| Genre | undergraduate thesis |
| Language | Croatian |
| Defense date | 2018-09-28 |
| 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 type | text |
| Access condition | Open access |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:126:110142 |
