Article

The Zero Divisor Graph of 2 × 2 Matrices Over a Field

Published in: Quaestiones Mathematicae
Volume 39 , issue 7 , 2016 , pages: 977–990

DOI: 10.2989/16073606.2016.1241958

Author(s): Ali Reza Ashrafi Department of Pure Mathematics, Faculty of Mathematical Sciences, I.R. Iran , Adel Tadayyonfar Department of Pure Mathematics, Faculty of Mathematical Sciences, I.R. Iran

Keywords: Primary 13A99 , Secondary 16U99 , 05C50 , Primary 13A99 , Secondary 16U99 , 05C50

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Abstract

A zero divisor graph, Γ(R), is formed from a ring R by having each element of Z(R) \ {0} to be a vertex in the graph and having two vertices u and v adjacent if the corresponding elements from the ring are nonequal and have product equal to zero. In this paper, the structure of the zero-divisor graph of 2 × 2 matrices over a field, Γ(M2(F)), are completely determined.

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