Lattices of quotients of completely distributive lattices |
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| Authors: | He Wei Luo MaoKang |
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| Affiliation: | (1) Department of Mathematics, Nanjing Normal University, Nanjing, 210097, P.R.China;(2) Department of Mathematics, Sichuan University, Chengdu, 610064, P.R.China |
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| Abstract: | In this paper, we consider the complete lattice Q(L) of all quotients of a completely distributive lattice L. We show that Q(L) is not a completely distributive lattice even for L a completely distributive algebraic lattice. Some necessary and sufficient conditions for Q(L) to be a completely distributive lattice are given. Received February 26, 2003; accepted in final form January 17, 2005. |
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| Keywords: | 46E25 54C30 |
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