Solvable and nilpotent near-ring modules
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- by Gordon Mason PDF
- Proc. Amer. Math. Soc. 40 (1973), 351-357 Request permission
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
- Michael Barr, What is the center?, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 1–12. MR 0249479 J. Beidleman, On near-rings and near-ring modules, Doctoral Thesis, Pennsylvania State University, University Park, Pa., 1964.
- A. Fröhlich, Distributively generated near-rings. I. Ideal theory. II. Representation theory, Proc. London Math. Soc. (3) 8 (1958), 76–94, 95–108. MR 92774, DOI 10.1112/plms/s3-8.1.76
- R. R. Laxton, Prime ideals and the ideal-radical of a distributively generated near-ring, Math. Z. 83 (1964), 8–17. MR 159841, DOI 10.1007/BF01111100
Additional Information
- © Copyright 1973 American Mathematical Society
- 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