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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)

08A60 Unary algebras