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Algebra universalis

, Volume 57, Issue 2, pp 207–214 | Cite as

Finite lattices as relative congruence lattices of finite algebras

  • A. M. Nurakunov
Article

Abstract.

Let A be a finite algebra and \({\mathcal{Q}}\) a quasivariety. By \({\rm Con}_{{\mathcal{Q}}}\) A is meant the lattice of congruences θ on A with \(A/\theta \in {\mathcal{Q}}\). For any positive integer n, we give conditions on a finite algebra A under which for any n-element lattice L there is a quasivariety \({\mathcal{R}}\) such that \({\rm Con}_{R} A \cong L\).

2000 Mathematics Subject Classification:

Primary 08A30 Secondary 08C15 

Keywords and phrases:

quasivariety finite lattice relative congruence lattice 

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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Chui pr., 265a, Institute of MathematicsNational Academy of ScienceBishkekKyrghyz Republic

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