algebra universalis

, Volume 54, Issue 1, pp 121–127 | Cite as

Lattices of quotients of completely distributive lattices

  • He Wei
  • Luo MaoKang
Original Paper


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.

Mathematics Subject Classification (2000).

46E25 54C30 

Keywords and phrases.

Quotient lattice completely distributive 


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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Normal UniversityNanjingP.R.China
  2. 2.Department of MathematicsSichuan UniversityChengduP.R.China

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