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Zbl 0636.03059
Meng, Daoji
BCI-algebras and Abelian groups. (English)
[J] Math. Jap. 32, 693-696 (1987). ISSN 0025-5513

If the BCK-part of a BCI-algebra (X,$\cdot,0)$ is trivial, then $(X,+)$, where $x+y=x(Oy)$, is an abelian group. Conversely, if $(X,+)$ is an abelian group, then (X,$\cdot,O)$, where $xy=y-x$, is a BCI-algebra and its BCK-part is trivial. \par 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)).
[W.A.Dudek]

MSC 2000:: *03G25 Other algebras related to logic
20L05 Groupoids
08A05 Structure theory of general algebraic systems

Keywords: BCK-part; BCI-algebra; abelian group

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