Monounary algebras with same quasiorders or retracts

• Autorzy: Jakubíková-Studenovská D. , Petrejčíková M. , Pócs J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

monounary algebra; quasiorder; congruence; retract

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 3
• Strony: 481--496
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Jakubíková-Studenovská D.

autor

Petrejčíková M.

autor

Pócs J.

• Institute Of Mathematics, P.J.Šafárik University Jesenná 5 041 54 Košice, Slovakia,

Bibliografia

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