On Prime E-ideals of Almost Distributive Lattices

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N. Rafi, Y. Monikarchana, Ravikumar Bandaru, Aiyared Iampan

Abstract

In an almost distributive lattice (ADL), the idea of E-ideals is introduced, and their properties are discussed. In terms of a congruence, an equivalence is established between the minimal prime Eideals of an ADL and its quotient ADL. Finally, topological investigations are performed on prime E-ideals and minimal prime E-ideals.

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References

  1. G. Birkhoff, Lattice theory, Colloq. Publ. XXV, Amer. Math. Soc. Providence, 1967.
  2. W.H. Cornish, Normal lattices, J. Aust. Math. Soc. 14 (1972), 200-215. https://doi.org/10.1017/s1446788700010041.
  3. G. Grätzer, General lattice theory, Birkhäuser, Basel, 1978. https://doi.org/10.1007/978-3-0348-7633-9.
  4. A.P. Phaneendra Kumar, M. Sambasiva Rao, K. Sobhan Babu, Generalized prime D-filters of distributive lattices, Arch. Math. 57 (2021), 157-174. https://doi.org/10.5817/AM2021-3-157.
  5. G.C. Rao, Almost distributive lattices, Doctoral Thesis, Department of Mathematics, Andhra University, Visakhapatnam, 1980.
  6. G.C. Rao, S. Ravi Kumar, Minimal prime ideals in an ADL, Int. J. Contemp. Math. Sci. 4 (2009), 475-484
  7. G.C. Rao, S. Ravi Kumar, Normal almost distributive lattices, Southeast Asian Bull. Math. 32 (2008), 831-841.
  8. G.C. Rao, M. Sambasiva Rao, Annulets in almost distributive lattices, Eur. J. Pure Appl. Math. 2 (2009), 58-72.
  9. U.M. Swamy, G.C. Rao, Almost distributive lattices, J. Aust. Math. Soc. 31 (1981), 77-91. https://doi.org/10.1017/s1446788700018498.