Zero-Divisor Graphs of Nearrings and Semigroups

G. Alan Cannon (), Kent M. Neuerburg () and Shane P. Redmond ()
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G. Alan Cannon: Southeastern Louisiana University, Department of Mathematics
Kent M. Neuerburg: Southeastern Louisiana University, Department of Mathematics
Shane P. Redmond: Eastern Kentucky University, Department of Mathematics

A chapter in Nearrings and Nearfields, 2005, pp 189-200 from Springer

Abstract: Abstract Zero-divisor graphs of rings have been developed and explored by D. F. Anderson and Livingston, Redmond, and others ([4], [5], [15], [17]). Additionally, these ideas have been adapted to semigroups by DeMeyer, McKenzie, and Schneider [10]. Results concerning the properties of graphs of semigroups are presented. All possible zero-divisor graphs of nearrings with identity in which the graph has less than five vertices are classified, and the additive group of each nonring is identified. Following the example of [7], we include a table of nearrings with identity of orders between sixteen and thirty-one.

Keywords: zero-divisor graph; nearring; semigroup (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/1-4020-3391-5_8

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