On BCI-algebras with condition (S) (Q2707056)

Let \(X\) be BCI-algebra with condition (S). A non-empty subset of \(X\) is called a subalgebra if it is a subalgebra with respect to both the BCI operation and the condition (S) operation. The authors characterise when the \(p\)-semisimple part of \(X\) is a subalgebra. They then show that under this condition, \(X\) is isomorphic to the product of a BCK-algebra with condition (S) and a \(p\)-semisimple BCI-algebra.