Weakly-Heyting Almost Distributive Lattices

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DOI: https://doi.org/10.28924/2291-8639-24-2026-90
Published: Mar 19, 2026
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M. V. Ratnamani, S. Ramesh, V. V. V. S. S. P. S. Srikanth, Ravikumar Bandaru, Thiti Gaketem, Weakly-Heyting Almost Distributive Lattices, Int. J. Anal. Appl., 24 (2026), 90.

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M. V. Ratnamani, S. Ramesh, V. V. V. S. S. P. S. Srikanth, Ravikumar Bandaru, Thiti Gaketem

Abstract

The primary goal of this article is to define the Weakly-Heyting Almost Distributive Lattice (WHADL), a novel algebraic structure that extends weakly-Heyting algebras within the broader class of almost distributive lattices. Through illustrative examples, we demonstrate that Heyting Almost Distributive Lattices (HADLs) and WHADLs are distinct structures. Furthermore, we identify and examine several sets of properties that characterize WHADLs, investigate their internal structure via principal ideals, and establish a necessary condition under which an WHADL becomes a HADL.

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