Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지

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)
  • Published : 1988.06.20
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords