Displaying similar documents to “Chain conditions in modular lattices”

S-extremal strongly modular lattices

Gabriele Nebe, Kristina Schindelar (2007)

Journal de Théorie des Nombres de Bordeaux

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S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only finitely many s-extremal strongly modular lattices of even minimum.

Orthomodular Lattices

Elżbieta Mądra, Adam Grabowski (2008)

Formalized Mathematics

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The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence...