• Korean Journal of Mathematics
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• v.16 no.3
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• pp.379-388
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• 2008

We introduce countably strong inclusions ${\triangleleft}=({\triangleleft}_1,\;{\triangleleft}_2)$ on a biframe $L=(L_0,\;L_1,\;L_2)$ and i-strongly regular ${\sigma}$-ideals (i =1, 2) and then using them, we construct biframe $Lindel{\ddot{o}}fication$ of L. Furthermore, we obtain a sufficient condition for which L has a unique countably strong inclusion.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.87-100
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• 2007

We introduce a concept of countably strong inclusions ${\triangleleft}$ and that of ${\triangleleft}-{\sigma}$-ideals and prove that the subframe $S({\triangleleft})$ of the frame ${\sigma}IdL$ of ${\sigma}$-ideals is a Lindel$\ddot{o}$fication of a frame L. We also deal with conditions for which the converse holds. We show that any countably approximating regular $D({\aleph}_1)$ frame has the smallest countably strong inclusion and any frame which has the smallest $D({\aleph}_1)$ Lindel$\ddot{o}$fication is countably approximating regular $D({\aleph}_1)$.