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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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] Michael Barr, What is the center?, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 1–12. MR 0249479
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Keywords: Near-ring module, center, solvable, nilpotent
Article copyright: © Copyright 1973 American Mathematical Society