Geometric Zero-Divisor Graphs

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Hadian Jazi, Majid | 2011

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 42738 (02)
University: Sharif University of Technology
Department: mathematics
Advisor(s): Shahshahani, Siavash; Shahshahani, Mehrdad
Abstract:
In this thesis, zero-divisor ideal graphs and geometric zero-divisor graphs are introduced and are partially studied. We begin by studying the relation between the zero-divisor graph and zero-divisor ideal graph associated to principal ideal rings. We also investigate some of the basic properties of the zero-divisor ideal graphs, including their girth and diameter. Then, we introduce the geometric zero-divisor graphs associated to reduced schemes and study their basic properties to some extent. Finally, we conclude by characterizing all reduced schemes whose associated geometric zero-divisor graph contains a vertex which is adjacent to all other vertices
Keywords:
Zero-divisor Ideal Graph ; Geometric Zero-divisor Graph ; Reduced Shemes