| Title | Neke klase komutativnih prstena s jedinicom |
| Author | Nikolina Kelava |
| Mentor(s) | Tanja Vučičić (thesis advisor)
|
| Abstract | U ovom radu su opisane tri klase komutativnih prstena s jedinicom: euklidske domene, domene glavnih ideala i domene jedinstvene faktorizacije. Navedena su neka njihova zajednička, kao i specifična svojstva. Zajedničko svojstvo je npr. egzistencija najvećeg zajedničkog djelitelja. Specifično, u euklidskoj domeni postoji algoritam za određivanje najvećeg zajedničkog djelitelja. Za promatrane klase utvrđuje se međusobni odnos oblika niza skupovnih inkluzija: polja, euklidske domene, domene glavnih ideala, domene jedinstvene faktorizacije, integralne domene, gdje su sva sadržavanja prava. Naši važni primjeri su prsten cijelih brojeva Z i prsten polinoma F[x] s koecijentima iz danog polja F. U radu je pokazano da su neke općepoznate činjenice o svojstvima cijelih brojeva i polinoma iz Z[x] i Q[x] specijalni slučajevi tvrdnji koje vrijede u općenitijim prstenima. |
| Keywords | Euclidean domain principal ideal domain unique factorization domain |
| Parallel title (English) | Some classes of commutative rings with identity |
| Committee Members | Tanja Vučičić (committee chairperson)
Anka Golemac (committee member)
Tea Martinić Bilać (committee member)
|
| Granter | University of Split
University of Split, Faculty of science |
| Lower level organizational units | Department of Mathematics |
| Place | Split |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics and Computer Science; specializations in: major in teaching |
| Study specialization | major in teaching |
| Academic title abbreviation | mag. educ. math. et inf. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2017-04-05 |
| Parallel abstract (English) | In this thesis three classes of commutative rings with identity are described, that being Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains. Some of their common properties are given, as well as the specic ones. For instance, the existence of greatest common divisor is one of their common properties; specically, in Euclidean Domains g.c.d. can be computed algorithmically. The interrelation between classes proves to be a chain of inclusions elds, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains, integral domains, where all containments are proper. Our principal examples are the ring Z of integers and the polynomial rings F[x] with coe¢ cients in some eld F: It is shown that some well-known theorems on the integers Z and polynomials from Z[x] and Q[x] are special cases of results valid for more general rings. |
| Parallel keywords (Croatian) | euklidska domena domena glavnih ideala domena jedinstvene faktorizacije |
| Resource type | text |
| Access condition | Access restricted to students and staff of home institution |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:166:771242 |
