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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
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

[1]Frolich, A., ‘Distributively generated near rings (I. ideal theory)’, Proc. London Math. Soc. (3) 8 (1958), 76–94.CrossRefGoogle Scholar
[2]Gonshor, H., ‘On abstract affine near-rings’, Pacific J. Math. 14 (1964), 1237–1240.CrossRefGoogle Scholar
[3]Ligh, S., ‘On boolean near-rings’, Bull Austral. Math. Soc. 1 (1969), 375–379.CrossRefGoogle Scholar
[4]Ligh, S., ‘The structure of a special class of near-rings’, J. Austral. Math. Soc. 13 (1972) 141–146.CrossRefGoogle Scholar
[5]Murty, C. V. L. N., ‘On strongly regular near-rings’, Algebra and its Applications, (Lecture Notes in Pure and Appl. Math. 91, Dekker, 1984, pp. 293–300).Google Scholar
[6]Pilz, G., Near-rings, (North-Holland, 1977).Google Scholar
[7]Reddy, Y. N. and Murty, C. V. L. N., ‘On strongly regular near-rings’, Proc. Edinburgh Math. Soc. 27 (1984), 61–64.CrossRefGoogle Scholar
[8]Subrahmanyam, N. V., ‘Boolean semirings’, Math. Ann. 148 (1962), 395–401.CrossRefGoogle Scholar