This article is the second part of an essay dedicated to lattices freelygenerated by posets within a variety. The first part dealt with four easyvarieties while this part is concerned with finitely generated varieties. Herewe present a method of constructing a subdirect product L of a finite family Fof finite lattices, exploiting a set of special elements of L deducted from F.This method is applied to free lattices generated by posets within finitelygenerated varieties, where in the case of the variety of modular lattices, weelaborate an efficient algorithm to compute the modular lattice M freelygenerated by a poset. For some posets of order six, the cardinality of M islisted.
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