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On iterated direct limits of a monounary algebra. (English) Zbl 0912.08003
Contributions to general algebra 10. Selection of lectures given at the conference on general algebra, Klagenfurt, Austria, May 29–June 1, 1997. Klagenfurt: Verlag Johannes Heyn. 189-195 (1998).
For an algebra $$A$$, $$\text{Ł}{L}(A)$$ denotes the set $$\{\text{Ł}\lim(A_{i})\}$$ of direct limits, where the $$A_i$$ are isomorphic to $$A$$. It is proved that $$\text{Ł} L(A)\not=\text{Ł}{L}(\text{Ł} L(A))$$ for every element $$A$$ from the following class $$\mathcal A$$ of monounary algebras: Let $$B_0$$ and $$D_0$$ are some connected monounary algebras without cycles such that there exist no homomorphisms from $$B_0$$ to $$D_0$$. Then each $$A$$ should contain a subalgebra isomorphic to the disjoint union of $$B_0$$ and $$D_0$$ and if $$E$$ is a maximal connected subalgebra of $$A$$ then either $$E\cong B_0$$ or $$E\cong D_0$$.
For the entire collection see [Zbl 0889.00019].
Reviewer: P.Normak (Tallinn)

##### MSC:
 08A60 Unary algebras
##### Keywords:
monounary algebra; direct limit