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Some properties of retract lattices of monounary algebras

In: Mathematica Slovaca, vol. 62, no. 2
D. Studenovská - Jozef Pócs
Detaily:
Rok, strany: 2012, 169 - 186
Kľúčové slová:
monounary algebra, retract, retract lattice
O článku:
Necessary and sufficient conditions for a connected monounary algebra $(A,f)$, under which the lattice $\mathbf{R}\emptyset(A,f)$ of all retracts of $(A,f)$ (together with $\emptyset$) is algebraic, are proved. Simultaneously, all connected monounary algebras in which each retract is a union of completely join-irreducible elements of $\mathbf{R}\emptyset(A,f)$ are characterized. Further, there are described all connected monounary algebras $(A,f)$ such that the lattice $\mathbf{R}\emptyset(A,f)$ is complemented. In this case $\mathbf{R}\emptyset(A,f)$ forms a boolean lattice.
Ako citovať:
ISO 690:
Studenovská, D., Pócs, J. 2012. Some properties of retract lattices of monounary algebras. In Mathematica Slovaca, vol. 62, no.2, pp. 169-186. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0002-4

APA:
Studenovská, D., Pócs, J. (2012). Some properties of retract lattices of monounary algebras. Mathematica Slovaca, 62(2), 169-186. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0002-4
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