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Proceedings of the American Mathematical Society

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Solvable and nilpotent near-ring modules

Author: Gordon Mason
Journal: Proc. Amer. Math. Soc. 40 (1973), 351-357
MSC: Primary 16A76
MathSciNet review: 0320094
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Abstract: The center of a unital near-ring module $ {}_RM$ is defined, leading to the construction of a lower central series and a definition of $ R$-nilpotence. Likewise a suitable definition of commutators yields a derived series and $ R$-solvability. When $ (R, + )$ is generated by elements which distribute over $ M$ the $ R$-nilpotence ($ R$-solvability) is shown to coincide with the nilpotence (solvability) of the underlying group. In this case, nilpotence has implications for $ R$-normalizers and the Frattini submodule.

References [Enhancements On Off] (What's this?)

  • [1] M. Barr, What is the center? Reports of the Midwest Category Seminar III, Lecture Notes in Math., vol. 106, Springer-Verlag, Berlin and New York, 1969, pp. 1-12. MR 0249479 (40:2724)
  • [2] J. Beidleman, On near-rings and near-ring modules, Doctoral Thesis, Pennsylvania State University, University Park, Pa., 1964.
  • [3] A. Frohlich, Distributively generated near-rings, I. Ideal theory, Proc. London Math. Soc. (3)8(1958), 76-94. MR 19, 1156. MR 0092774 (19:1156b)
  • [4] R. Laxton, Prime ideals and the ideal-radical of a distributively generated near-ring, Math. Z. 83 (1964), 8-17. MR 28 #3057. MR 0159841 (28:3057)

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Keywords: Near-ring module, center, solvable, nilpotent
Article copyright: © Copyright 1973 American Mathematical Society

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