Geodesic
Reflexivity of bilattices
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 995-1000

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MR Zbl
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.
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.
DOI : 10.1007/s10587-013-0067-4
Classification : 47A15, 47L99
Keywords: reflexive algebra; reflexive lattice; subspace lattice; bilattice 
Kliś-Garlicka, Kamila. Reflexivity of bilattices. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 995-1000. doi: 10.1007/s10587-013-0067-4
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