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In this note we prove: If a subdirect product of finitely many finite projective geometries has the cover-preserving embedding property, then so does each factor.

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. I. lattices of convex sets . Acta Sci. Math.(Szeged) 52 , 1-2 ( 1988 ), 35 – 45 . [23] Jakubík , J . Modular lattices of locally finite length . Acta Sci. Math.(Szeged) 37 , 1-2 ( 1975 ), 79 – 82 . [24] Koh , K. M . On the length of the

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Abstract  

The concept of `adjunct' operation of two lattices with respect to a pair of elements is introduced. A structure theorem namely, `A finite lattice is dismantlable if and only if it is an adjunct of chains' is obtained. Further it is established that for any adjunct representation of a dismantlable lattice the number of chains as well as the number of times a pair of elements occurs remains the same. If a dismantlable lattice L has n elements and n+k edges then it is proved that the number of irreducible elements of L lies between n-2k-2 and n-2. These results are used to enumerate the class of lattices with exactly two reducible elements, the class of lattices with n elements and upto n+1 edges, and their subclasses of distributive lattices and modular lattices.

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