%0 Journal Article %1 poeschel/etal:2011 %A Jakubíková-Studenovská, Danica %A Pöschel, Reinhard %A Radeleczki, Sándor %D 2011 %I Springer Netherlands %J Order %K 2011 jakubikova-studenovska journal poeschel publication radeleczki %P 481-497 %R 10.1007/s11083-010-9186-9 %T The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras %U http://dx.doi.org/10.1007/s11083-010-9186-9 %V 28 %X 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 we characterize the intersection of compatible linear extensions of r by several equivalent conditions and generalize these results to compatible quasiorders of . We show that the lattice 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 and .

@article{poeschel/etal:2011, 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 we characterize the intersection of compatible linear extensions of r by several equivalent conditions and generalize these results to compatible quasiorders of . We show that the lattice 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 and .}, added-at = {2011-11-28T13:01:31.000+0100}, affiliation = {Institute of Mathematics, P. J. Šafárik University, Košice, Slovakia}, author = {Jakubíková-Studenovská, Danica and Pöschel, Reinhard and Radeleczki, Sándor}, biburl = {https://www.bibsonomy.org/bibtex/2101e346ad7883d71a412cd8e516e4a2b/algebradresden}, doi = {10.1007/s11083-010-9186-9}, interhash = {e1447dec479218e1ff77b56210d1ca4f}, intrahash = {101e346ad7883d71a412cd8e516e4a2b}, issn = {0167-8094}, issue = {3}, journal = {Order}, keyword = {Mathematics and Statistics}, keywords = {2011 jakubikova-studenovska journal poeschel publication radeleczki}, pages = {481-497}, publisher = {Springer Netherlands}, timestamp = {2011-11-28T13:01:31.000+0100}, title = {The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras}, url = {http://dx.doi.org/10.1007/s11083-010-9186-9}, volume = 28, year = 2011 }