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Green’s relations in the commutative centralizers of monounary algebras

Jakubíková-Studenovská D., Šuličová M.

Demonstratio Mathematica

2015

Vol. 48, nr 4

536--545

The paper deals with the monounary algebras for which the second centralizer equals the first centralizer. We describe Green’s relations on the semigroup C, where C is the centralizer of such algebra.

Monounary algebras with same quasiorders or retracts

Jakubíková-Studenovská D., Petrejčíková M., Pócs J.

Demonstratio Mathematica

2011

Vol. 44, nr 3

481-496

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.