On the extended annihilator graph of a commutative ring

چکیده مقاله

In this paper we present a new graph that is closely related to the classical zero-divisor graph. The extended annihilator graph of a commutative ring R is the graph  with vertices of   and two nonzero distinct zero divisors x and y of R are adjacent whenever there exist two nonnegative integers n and m such that  with  and . It follows that each edge (path) of the extended zero divisor graph  is an edge (path) of  . We show that  is connected with diameter at most two.

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