International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Birkhoff Centre of Paradistributive Latticiods

  • Ramesh Sirisetti
  • Satyanarayana Rao Kola
  • Ravikumar Bandaru
  • Thiti Gaketem*

    * Corresponding author

    Abstract

    We study the Birkhoff centre B(V) of a Paradistributive Latticoid (PDL) V. Assuming the existence of a greatest element and at least one minimal element, we prove that B(V) forms a relatively complemented sub-PDL and derive a decomposition theorem characterizing its elements via direct products. We establish functoriality of B(−) with respect to products and lattice-quotients enforcing commutativity, and we show a bijection between B(V) and complemented principal ideals of V. For associative PDLs, we obtain a correspondence between B(V) and factor-congruences, hence direct decompositions. The results extend earlier work on almost distributive lattices to the broader framework of PDLs and connect with the theory of normal PDLs.

    How to Cite

    R. Sirisetti, S. R. Kola, R. Bandaru, T. Gaketem, Birkhoff Centre of Paradistributive Latticiods, Int. J. Anal. Appl. 23 (2025), 295. https://doi.org/10.28924/2291-8639-23-2025-295

    BibTeX
    @article{Sirisetti2025,
  author  = {Sirisetti, Ramesh and Kola, Satyanarayana Rao and Bandaru, Ravikumar and Gaketem, Thiti},
  title   = {Birkhoff Centre of Paradistributive Latticiods},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {295},
  doi     = {10.28924/2291-8639-23-2025-295}
}

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