Abstract
This paper is a continuation of [6], where irreducibility in the sense of Duffus and Rival (DR-irreducibility) of monounary algebras was defined. The definition is analogous to that introduced by Duffus and Rival [1] for the case of posets. In [6] we found all connected monounary algebras A possessing a cycle and such that A is DR-irreducible. The main result of the present paper is Thm. 4.1 which describes all connected monounary algebras A without a cycle and such that A is DR-irreducible. Other types of irreducibility of monounary algebras defined by means of the notion of a retract were studied in [2]-[5].
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