Kyungpook Mathematical Journal
- 제28권1호
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- Pages.39-44
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- 1988
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- 1225-6951(pISSN)
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- 0454-8124(eISSN)
EXAMPLES OF NEAR-RING NEUMANN SYSTEMS
- McQuarrie, B.C. (Department of Mathematical Sciences Worcester Polytechnic institute) ;
- Malone, J.J. (Department of Mathematical Sciences Worcester Polytechnic institute)
- 발행 : 1988.06.20
초록
In 1940, B. H. Neumann, working with a system more general than a near-field, proved that the additive group of such a system (and of a near-field) is commutative. The algebraic structure he used is known as a Neumann system (N-system). Here, the prime N-systems are classified and for each possible characteristic, examples of N-systems which are neither near-fields nor rings are given. It is also shown that a necessary condition for the set of all odd polynomials over GF(p) to be an N-system is that p is a Fermat prime.
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