Real Fields

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.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 homomorphism