Monounary algebras with same quasiorders or retracts

Demonstratio mathematica

article

Danica Jakubíková-Studenovská¹  Mária Petrejčíková¹  Jozef Pócs² 

[1] Institute of Mathematics, P. J. Šafárik University;Mathematical Institute, Slovak Academy of Sciences

关键词: monounary algebra;    quasiorder;    congruence;    retract;   

DOI  :  10.1515/dema-2013-0326

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

Let ( A, f ) be a monounary algebra. We describe all monounary algebras ( A, g ) having the same set of quasiorders, Quord( A, f ) = Quord( A, g ). It is proved that if Quord( A, f ) does not coincide with the set of all reflexive and transitive relations on the set A and ( A, f ) contains no cycle with more than two elements, then f is uniquely determined by means of Quord( A, f ). In the opposite case, Quord( A, f ) = Quord( A, g ) if and only if Con( A, f ) = Con( A, g ). Further, we show that, except the case when Quord( A, f ) coincides with the set of all reflexive and transitive relations, if the monounary algebras ( A, f ) and ( A, g ) have the same quasiorders, then they have the same retracts. Next we characterize monounary algebras which are determined by their sets of retracts and connected monounary algebras which are determined by their sets of quasiorders.

【 授权许可】

CC BY