Rao, G. C.; Alamneh, Mihret Post almost distributive lattices. (English) Zbl 1438.06028 Southeast Asian Bull. Math. 43, No. 1, 121-132 (2019). Summary: The concepts of chain based almost distributive lattices (ADLs) were introduced in our earlier papers. In this paper, we introduce a Post almost distributive lattice (Post ADL) with a chain base and we prove the basic properties and facts on a Post ADL related to a \({P_0}\)-ADL, a \({P_1}\)-ADL, a \({P_2}\)-ADL and a \(B\)-ADL (\(BL\)-ADL). We prove a necessary and sufficient condition for an ADL to become a Post ADL and finally prove that a \({P_2}\)-ADL of order \(n\) is almost isomorphic to a direct product of Post ADLs of maximum order \(n\). MSC: 06D25 Post algebras (lattice-theoretic aspects) 03G20 Logical aspects of Łukasiewicz and Post algebras 06D75 Other generalizations of distributive lattices Keywords:almost distributive lattice; chain base; disjoint representation; monotone representation; pseudo-supplement PDFBibTeX XMLCite \textit{G. C. Rao} and \textit{M. Alamneh}, Southeast Asian Bull. Math. 43, No. 1, 121--132 (2019; Zbl 1438.06028)