On ideal extensions of partial monounary algebras

summary:In the present paper we introduce the notion of an ideal of a partial monounary algebra. Further, for an ideal $(I,f_I)$ of a partial monounary algebra $(A,f_A)$ we define the quotient partial monounary algebra $(A,f_A)/(I,f_I)$. Let $(X,f_X)$, $(Y,f_Y)$ be partial monounary algebras. We describe all partial monounary algebras $(P,f_P)$ such that $(X,f_X)$ is an ideal of $(P,f_P)$ and $(P,f_P)/(X,f_X)$ is isomorphic to $(Y,f_Y)$