If the BCK-part of a BCI-algebra (X, is trivial, then , where , is an abelian group. Conversely, if is an abelian group, then (X,, where , is a BCI-algebra and its BCK-part is trivial.
Reviewer’s remark: This result was presented by the reviewer during the All-Polish Conference on Universal Algebra and its Applications, Opole, May 1985 (see Materiały or Demonstr. Math. (appear)).