Advances and Applications in Discrete Mathematics
Volume 10, Issue 1, Pages 49 - 64
(July 2012)
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ZERO-DIVISOR GRAPHS OF NON-COMMUTATIVE RINGS
Kukil Kalpa Rajkhowa and Helen K. Saikia
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Abstract: We investigate the characteristics of zero-divisor graph of non-commutative ring. A set of relations on vertex set of directed graphs encloses the observations in the discussion. Annihilators play a vital role for the continuation. The idea of orthogonality is a prominent tool for our interpretation. Different directions are brought to attention in orthogonal condition. Orthogonality leads to the complemented graph. Some basic concepts of ring theory help to an extent. |
Keywords and phrases: non-commutative rings, zero-divisor, annihilator, invertible element, regular element, directed graph, orthogonal, complement. |
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