ON HOLOMORPHY OF FENYVES BCI-ALGEBRAS

E. ILOJIDE, T. G. JAIYEOLA, M. O. OLATINWO

Abstract


Fenyves BCI-algebras are BCI-algebras that satisfy the Bol-Moufang identities. In this paper, the holomorphy of BCI-algebras are studied. It is shown that whenever a loop and its holomorph are BCI-algebras, the former is $p$-semisimple if and only if the latter is $p$-semisimple. Whenever a loop and its holomorph are BCI-algebras, it is established that the former is a BCK-algebra if and only if the latter has a BCK-subalgebra. Moreover, the holomorphy of the associative and some non-associative Fenyves BCI-algebras are also studied.

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