Birkhoff Centre of Paradistributive Latticiods

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DOI: https://doi.org/10.28924/2291-8639-23-2025-295
Published: Nov 13, 2025
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Ramesh Sirisetti, Satyanarayana Rao Kola, Ravikumar Bandaru, Thiti Gaketem, Birkhoff Centre of Paradistributive Latticiods, Int. J. Anal. Appl., 23 (2025), 295.

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Ramesh Sirisetti, Satyanarayana Rao Kola, Ravikumar Bandaru, Thiti Gaketem

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.

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