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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The lattice of left ideals in a centralizer near-ring is distributive
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by Kirby C. Smith PDF
Proc. Amer. Math. Soc. 85 (1982), 313-317 Request permission

Abstract:

A decomposition theorem for a left ideal in a finite centralizer near-ring is established. This result is used to show that the lattice of left ideals in a finite centralizer near-ring is distributive.
References
  • Gerhard Betsch, Primitive near-rings, Math. Z. 130 (1973), 351–361. MR 325706, DOI 10.1007/BF01179162
  • Nathan Jacobson, Basic algebra. I, W. H. Freeman and Co., San Francisco, Calif., 1974. MR 0356989
  • J. Maxson and K. C. Smith, Centralizer near-rings: Left ideals and $0$-primitivity, Proc. Roy. ish Acad. Sect. A (to appear). J. Maxson, M. R. Pettet and K. C. Smith, On semisimple rings that are centralizer near-rings, acific J. Math, (to appear).
  • Günter Pilz, Near-rings, North-Holland Mathematics Studies, No. 23, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications. MR 0469981
  • Wielandt, Unpublished manuscripts from the years 1937-1952.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 313-317
  • MSC: Primary 16A76; Secondary 06D10
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656091-5
  • MathSciNet review: 656091