The Grobner Annihilator Graph of a Ring

Date of Award

2009

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Poimenidou, Eirini

Keywords

Grobner Bases, Zero Divisor Graph, Annihilators

Area of Concentration

Mathematics

Abstract

In recent years, graph theory has been used as a tool to study rings in the form of several different graphs, many of which are based on the zero divisor structure of the ring. We define here the annihilator graph of a ring to try to harness the best possible graphical representation of a ring. This paper lays the foundation for the theory of annihilator graphs and the extension of them to a more general form, the Grobner annihilator graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Grobner annihilator graph of that ring.

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