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Boolean near-rings and weak commutativity

Published online by Cambridge University Press:  09 April 2009

D. J. Hansen  and
Jiang Luh
D. J. Hansen
Affiliation:
Department of Mathematics, North Carolina State University Raleigh, North Carolina 27695-8205, U.S.A.
Jiang Luh
Affiliation:
Department of Mathematics, North Carolina State University Raleigh, North Carolina 27695-8205, U.S.A.
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Abstract

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It is shown that every boolean right near-ring R is weakly commutative, that is, that xyz = xzy for each x, y, z ∈ 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 to be isomorphic to a particular collection of functions which form a boolean near-ring with respect to the customary operations of addition and composition of mappings.

MSC classification

Secondary: 06E20: Ring-theoretic properties

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 1 , August 1989 , pp. 103 - 107
Copyright
Copyright © Australian Mathematical Society 1989

References

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