The notion of p-semisimple pseudo-BCI-algebras is introduced and its characterizations are established. It is shown that the p-semisimple pseudo-BCI-algebras and the groups are categorically equivalent. The set At(X) of atoms of a pseudo-BCI-algebra X is studied and it is proved that At(X) is a p-semisimple pseudo-BCI-algebra. There is shown that a pseudo-BCIalgebra X is p-semisimple if and only if X = At(X).
Keywords: pseudo-BCI-algebra, p-semisimple pseudo-BCI-algebra, atom, pseudo-BCK-algebra, group