ANALIZA KOMUTATIVNIH PRSTENA PRIDRUŽIVANJEM SIMPLICIJALNIH KOMPLEKSA

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ANALIZA KOMUTATIVNIH PRSTENA PRIDRUŽIVANJEM SIMPLICIJALNIH KOMPLEKSA

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dc.contributor.advisor Petrović, Zoran
dc.contributor.author Milošević, Nela
dc.date.accessioned 2017-02-02T17:00:42Z
dc.date.available 2017-02-02T17:00:42Z
dc.date.issued 2015
dc.identifier.uri http://hdl.handle.net/123456789/4421
dc.description.abstract This dissertation examines simplicial complexes associated with commutative rings with unity. In general, a combinatorial object can be attached to a ring in many di erent ways, and in this dissertation we examine several simplicial complexes attached to rings which give interesting results. Focus of this thesis is determining the homotopy type of geometric realization of these simplicial complexes, when it is possible. For a partially ordered set of nontrivial ideals in a commutative ring with identity, we investigate order complex and determine its homotopy type for the general case. Simplicial complex can also be associated to a ring indirectly, as an independence complex of some graph or hypergraph which is associated to that ring. For the comaximal graph of commutative ring with identity we de ne its independence complex and determine its homotopy type for general commutative rings with identity. This thesis also focuses on the study of zero-divisors, by investigating ideals which are zero-divisors and de ning zero-divisor ideal complex. The homotopy type of geometric realization of this simplicial complex is determined for rings that are nite and for rings that have in nitely many maximal ideals. In this part of the thesis, we use the discrete Morse theory for simplicial complexes. The theorems proven in this dissertation are then applied to certain classes of commutative rings, which gives us some interesting combinatorial results. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2017-02-02T17:00:42Z No. of bitstreams: 1 Nela_Milosevic_Teza.pdf: 20621261 bytes, checksum: a454c4998ea8c68c8f237177fb4b8e18 (MD5) en
dc.description.provenance Made available in DSpace on 2017-02-02T17:00:42Z (GMT). No. of bitstreams: 1 Nela_Milosevic_Teza.pdf: 20621261 bytes, checksum: a454c4998ea8c68c8f237177fb4b8e18 (MD5) Previous issue date: 2015 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title ANALIZA KOMUTATIVNIH PRSTENA PRIDRUŽIVANJEM SIMPLICIJALNIH KOMPLEKSA en_US
mf.author.birth-date 1986-01-03
mf.subject.area Mathematics en_US
mf.subject.keywords simplicial complex, homotopy type, commutative rings, order complex, discrete Morse theory, zero divisors, comaximal graph en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee Lipkovski, Aleksandar
mf.contributor.committee Petrović, Zoran
mf.contributor.committee Petrić, Zoran
mf.contributor.committee Pucanović, Zoran
mf.university.faculty Mathematical Faculty en_US
mf.document.references 34 en_US
mf.document.pages 83 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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