### Über endliche, ordnungspolynomvollständige Verbände.

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Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety ${V}_{\sigma}$ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...

We characterize lattices with a complemented tolerance lattice. As an application of our results we give a characterization of bounded weakly atomic modular lattices with a Boolean tolerance lattice.

We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.

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