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The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras

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Abstract

Acyclic monounary algebras are characterized by the property that any compatible partial order r can be extended to a compatible linear order. In the case of rooted monounary algebras \({\cal A}=(A,f)\) we characterize the intersection of compatible linear extensions of r by several equivalent conditions and generalize these results to compatible quasiorders of \({\cal A}\). We show that the lattice \({\rm{Quord}}{\cal A}\) of compatible quasiorders is a disjoint union of semi-intervals whose maximal elements equal the intersection of their compatible quasilinear extensions. We also investigate algebraic properties of the lattices \({\rm{Quord}}{\cal A}\) and \({\rm{Con}}{\cal A}\).

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Correspondence to Reinhard Pöschel.

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D. Jakubíková-Studenovská was supported by Slovak VEGA grant 2/0194/10.

R. Pöschel and S. Radeleczki were supported by DFG grant 436 UNG 113/173/0-2.

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Jakubíková-Studenovská, D., Pöschel, R. & Radeleczki, S. The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras. Order 28, 481–497 (2011). https://doi.org/10.1007/s11083-010-9186-9

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  • DOI: https://doi.org/10.1007/s11083-010-9186-9

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