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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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Lattices all of whose congruences are neutral
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by Chinthayamma Malliah and S. Parameshwara Bhatta PDF
Proc. Amer. Math. Soc. 94 (1985), 49-51 Request permission

Abstract:

We derive a necessary condition for all congruences on a lattice to be neutral, and we show that a stronger condition of the same type characterizes relatively complemented lattices. We also find a condition necessary and sufficient for all congruences to be neutral.
References
    Chinthayamma Malliah and Parameshwara Bhatta, S., Generalizations of dually distributive and neutral ideals to convex sublattices. I, Notre Dame J. Formal Logic (submitted). —, Generalizations of dually distributive and neutral ideals to convex sublattices. II, Notre Dame J. Formal Logic (submitted). —, Lattices all of whose congruences are standard or distributive, Fund. Math. (submitted).
  • George Grätzer, General lattice theory, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel-Stuttgart, 1978. MR 504338
  • Iqbalunnisa, Normal, simple and neutral congruences on lattices, Illinois J. Math. 10 (1966), 227–234. MR 190046
  • M. F. Janowitz, A characterisation of standard ideals, Acta Math. Acad. Sci. Hungar. 16 (1965), 289–301 (English, with Russian summary). MR 186589, DOI 10.1007/BF01904837
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 49-51
  • MSC: Primary 06B10; Secondary 06C15
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781054-1
  • MathSciNet review: 781054