Abstract
We prove that the class of finite lattices embeddable into the subsemilattice lattices of semilattices which are (n-ary) trees can be axiomatized by identities within the class of finite lattices, whence it forms a pseudovariety.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 894–913, July–August, 2007.
Original Russian Text Copyright © 2007 Semenova M. V.
The author was supported by INTAS (Grant 03-51-4110), the joint DFG-RFBR project 06-01-04002, the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-4413.2006.1), a grant of the President of the Russian Federation for the Young Candidates of Sciences (Grant MK-3988.2007.1), and the Junior Researcher Support Grant of the Siberian Division of the Russian Academy of Sciences (No. 11).
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Semenova, M.V. On lattices embeddable into subsemigroup lattices. V. Trees. Sib Math J 48, 718–732 (2007). https://doi.org/10.1007/s11202-007-0073-6
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DOI: https://doi.org/10.1007/s11202-007-0073-6