Abstract
It is well-known that a boolean ring is commutative. In this note we show that a distributively generated boolean near-ring is multiplicatively commutative, and therefore a ring. This is accomplished by using subdirect sum representations of near-rings.
Publisher
Cambridge University Press (CUP)
Cited by
14 articles.
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1. BZS Near-Rings and Rings;Springer Proceedings in Mathematics & Statistics;2021
2. On some properties of near-rings;Arabian Journal of Mathematics;2020-11-22
3. Certain conditions under which near-rings are rings;Bulletin of the Australian Mathematical Society;1990-08
4. Boolean near-rings and weak commutativity;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1989-08
5. A note on semigroups in rings;Journal of the Australian Mathematical Society;1977-11