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Keywords:
reflexive algebra; reflexive lattice; subspace lattice; bilattice
reflexive algebra; reflexive lattice; subspace lattice; bilattice
Summary:
We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice $\mathcal {L}$ we may associate a bilattice $\Sigma _{\mathcal {L}}$. Similarly, having a bilattice $\Sigma $ we may construct a subspace lattice $\mathcal {L}_{\Sigma }$. Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.
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