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DR-irreducibility of connected monounary algebras with a cycle. (English) Zbl 1079.08500
If \(K\) is a class of monounary algebras then a monounary algebra \(A\) is called retract irreducible in \(K\) if, whenever \(A\) is a retract of the product of some algebras in \(K\), then \(A\) is a retract of one of these algebras. The author studies the so-called DR-irreducibility of monounary algebras. An algebra \(A\) is DR-irreducible if it is retract irreducible in the class of algebras isomorphic to retract of \(A\). In the paper, all connected monounary algebras with a cycle which are DR-irreducible are described.

MSC:
08A60 Unary algebras
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