ANALIZA PRSTENA I MODULA PRIDRUŽIVANJEM GRAFOVA

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ANALIZA PRSTENA I MODULA PRIDRUŽIVANJEM GRAFOVA

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dc.contributor.advisor Petrović, Zoran
dc.contributor.author Pucanović, S. Zoran
dc.date.accessioned 2013-03-04T09:30:58Z
dc.date.available 2013-03-04T09:30:58Z
dc.date.issued 2012
dc.identifier.uri http://hdl.handle.net/123456789/2489
dc.description.abstract This dissertation examines various properties of commutative rings and modules using algebraic combinatorial methods. If the graph is properly associated to a ring R or to an R-module M, then examination of its properties gives useful information about the ring R or R-module M. This thesis discusses the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with. The total graph of a module, a generalization of the total graph of a ring is presented. Various properties are proved and some relations to the total graph of a ring as well as to the zero-divisor graph are established. To gain a better understanding of clean rings and their relatives, the clean graph C¡(R) of a commutative ring with identity is introduced and its various proper- ties established. Further investigation of clean graphs leads to additional results concerning other classes of commutative rings. One of the topics of this thesis is the investigation of the properties of the cor- responding line graph L(T¡(R)) of the total graph T¡(R). The classi¯cation of all commutative rings whose line graphs of the total graph are planar or toroidal is given. It is shown that for every integer g ¸ 0 there are only ¯nitely many commutative rings such that °(L(T¡(R))) = g. Also, in this thesis all toroidal graphs which are intersection graphs of ideals of a commutative ring R are classi¯ed. An improvement over the previous results concerning the planarity of these graphs is presented. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2013-03-04T09:30:58Z No. of bitstreams: 1 Pucanovic_Zoran.pdf: 2059864 bytes, checksum: 869368aafc9af479a73a1605be719868 (MD5) en
dc.description.provenance Made available in DSpace on 2013-03-04T09:30:58Z (GMT). No. of bitstreams: 1 Pucanovic_Zoran.pdf: 2059864 bytes, checksum: 869368aafc9af479a73a1605be719868 (MD5) Previous issue date: 2012 en
dc.language.iso sr en_US
dc.publisher Belgrade en_US
dc.title ANALIZA PRSTENA I MODULA PRIDRUŽIVANJEM GRAFOVA en_US
mf.author.birth-date 16.06.1968.
mf.author.birth-place Zajecar
mf.author.birth-country Serbia
mf.subject.area Mathematics en_US
mf.subject.keywords commutative rings, clean rings, modules, zero-divisors, total graph, en_US
mf.subject.keywords clean graph, line graph, intersection graph, genus of a graph en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee Lipkovski, Aleksandar
mf.contributor.committee Kalajdžić, Gojko
mf.contributor.committee Čukić, Ljubomir
mf.university.faculty Mathematical en_US
mf.document.references 57 en_US
mf.document.pages 84 en_US
mf.document.location Belgrade en_US
mf.document.genealogy-project No en_US
mf.university Belgrade en_US

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