  We classify essential algebras whose irredundant non-refinable covers consist
of primal algebras. The proof is obtained by constructing one to one
correspondence between such algebras and partial orders on finite sets.
Further, we prove that for a finite algebra, it has an irredundant
non-refinable cover consists of primal algebras if and only if it is the both
congruence primal and arithmetical. Finally, we obtain combinatorial
description of congruence primal arithmetical algebras.
