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dc.contributor.authorAliniaeifard, Farid
dc.date.accessioned2013-09-05T15:06:51Z
dc.date.available2013-09-05T15:06:51Z
dc.date.issued2013-09-05
dc.identifier.urihttp://hdl.handle.net/10464/4958
dc.description.abstractWe associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.en_US
dc.language.isoengen_US
dc.publisherBrock Universityen_US
dc.subjectRingsen_US
dc.subjectGroup Ringsen_US
dc.subjectZero-Divisor Graphsen_US
dc.subjectAnnihilating-Ideal Graphsen_US
dc.titleRings, Group Rings, and Their Graphsen_US
dc.typeElectronic Thesis or Dissertationen_US
dc.degree.nameM.Sc. Mathematics and Statisticsen_US
dc.degree.levelMastersen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.degree.disciplineFaculty of Mathematics and Scienceen_US
dc.embargo.termsNoneen_US
refterms.dateFOA2021-08-03T02:17:52Z


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