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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0320094-5
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.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320094-5
Keywords: Near-ring module, center, solvable, nilpotent
Article copyright: © Copyright 1973 American Mathematical Society

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