J Austral Math Soc Ser A 47 pp103--107, 1989.

Boolean Near-Rings and Weak Commutativity

D. J. Hansen and Jiang Luh

Abstract

It is shown that every boolean right near-ring R is weakly commutative, that is, that xyz = xzy for each x, y, z Î R. In addition, an elementary proof is given of a theorem due to S. Ligh which states that a d.g. boolean near-ring is a boolean ring. Finally, a characterization theorem is given for a boolean near-ring with respect to the customary operations of addition and composition of mappings.

1980 AMS Subject Classification (1985 Revision): primary 16A76; secondary 06E20, 16A30, 16A32

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Authors

D. J. Hansen

Jiang Luh

Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, U.S.A.