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The Grbner Annihilator Graph of a Ring

Trevor McGuire

ISBN 10: 3639196058 / ISBN 13: 9783639196054
Published by VDM Verlag
New Condition: New Soft cover
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68 pages. Dimensions: 8.7in. x 5.9in. x 0.2in.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 dene 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 Grbner annihilator graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Grbner annihilator graph of that ring. We will state some concise results while also formally stating areas in which the author feels further research is needed. This work is an extension of recent work on Zero Divisor Graphs, and Annihilator graphs, with an emphasis on simultaneous generalizations of both. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9783639196054

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Bibliographic Details

Title: The Grbner Annihilator Graph of a Ring

Publisher: VDM Verlag

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title

Synopsis:

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 de¿ne 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 Gröbner annihilator graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Gröbner annihilator graph of that ring. We will state some concise results while also formally stating areas in which the author feels further research is needed. This work is an extension of recent work on Zero Divisor Graphs, and Annihilator graphs, with an emphasis on simultaneous generalizations of both.

About the Author:

Trevor McGuire is a graduate student at Louisiana State University in Baton Rouge, Louisiana. His research interests include Gröbner Bases, random Fibonacci sequences, and commutative algebra. In his spare time, he is an amateur astronomer and competes in Scrabble tournaments.

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