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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lattices all of whose congruences are neutral


Authors: Chinthayamma Malliah and S. Parameshwara Bhatta
Journal: Proc. Amer. Math. Soc. 94 (1985), 49-51
MSC: Primary 06B10; Secondary 06C15
MathSciNet review: 781054
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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 [Enhancements On Off] (What's this?)

  • [1] Chinthayamma Malliah and Parameshwara Bhatta, S., Generalizations of dually distributive and neutral ideals to convex sublattices. I, Notre Dame J. Formal Logic (submitted).
  • [2] -, Generalizations of dually distributive and neutral ideals to convex sublattices. II, Notre Dame J. Formal Logic (submitted).
  • [3] -, Lattices all of whose congruences are standard or distributive, Fund. Math. (submitted).
  • [4] George Grätzer, General lattice theory, Birkhäuser Verlag, Basel-Stuttgart, 1978. Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52. MR 504338 (80c:06001a)
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  • [6] M. F. Janowitz, A characterisation of standard ideals, Acta Math. Acad. Sci. Hungar. 16 (1965), 289–301 (English, with Russian summary). MR 0186589 (32 #4048)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781054-1
PII: S 0002-9939(1985)0781054-1
Article copyright: © Copyright 1985 American Mathematical Society