Monounary algebras with easy direct limits

Emilia Haluskova;


Let $\cal A$ be an algebra such that exactly algebras isomorphic to a retract of $\cal A$ can be constructed from $\cal A$ by direct limits. Then $\cal A$ is an algebra with easy direct limits called. We will prove that if $\cal A$ is a monounary one, then $\cal A$ is countable and the number of retracts of $\cal A$ is not equal to $\aleph _0$. Further, we will see that the number of non-isomorphic monounary algebras with easy direct limits is $2^{\aleph _0}$.

Vol. 19 (2018), No. 1, pp. 291-302

Download: MMN-1744