Retract irreducibility of connected monounary algebras II

Abstract

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Representation of Connected Monounary Algebras by Means of Irreducibles

“…Assume that (c2) is valid and that A is not irreducible. By 1.3, there are a, b ∈ A with a = b such that f (a) = f (b) = c. Then the condition (C4) from [4] is satisfied and in view of the construction 4.1 and the corresponding lemmas in [4] we obtain that A is representable by means of irreducibles (these irreducibles are isomorphic to $ ∞ ).…”

“…Connected monounary algebras which are retract irreducible in the above classes were characterized in [4], [5] and [6] as follows:…”

“…The author [5]- [10] dealt with these relations for monounary algebras. Let us denote by U (and U c , respectively) the class of all (all connected) monounary algebras.…”

“…In [5] and [4] all connected monounary algebras which are retract irreducible in the class U c were described. Next, in [6] all connected monounary algebras retract irreducible in the class U were found.…”

“…Next, in [6] all connected monounary algebras retract irreducible in the class U were found. In [10] it was proved that there exist connected monounary algebras which are not representable by means of connected monounary algebras which are retract irreducible in U c .…”