ON HOLOMORPHY OF FENYVES BCI-ALGEBRAS

Authors

  • E. ILOJIDE DEPARTMENT OF MATHEMATICS, FEDERAL UNIVERSITY OF AGRICULTURE, ABEOKUTA
  • T. G. JAIYEOLA DEPARTMENT OF MATHEMATICS, OBAFEMI AWOLOWO UNIVERSITY, ILE-IFE,
  • M. O. OLATINWO DEPARTMENT OF MATHEMATICS, OBAFEMI AWOLOWO UNIVERSITY, ILE-IFE,

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.

References

J. O. Adeniran (2005), On holomorphic theory of a

class of left Bol loops, Al.I.Cuza 51, 1, 23-28.

J. O. Adeniran, Y.T. Oyebo and D. Mohammed (2011), On

certain isotopic maps of central loops, Proyecciones Journal of Mathematics. 30(3), 303--318.

J. O. Ad'en'iran, T. G. Jaiy'ed ol'a and K. A. Idowu (2014), Holomorph of generalized Bol loops, Novi Sad Journal of Mathematics, 44 (1), 37--51.

R. H. Bruck (1944), Contributions to the theory of loops, Trans. Amer. Math. Soc. 55, 245--354.

R. H. Bruck and L. J. Paige (1956), Loops whose

inner mappings are automorphisms, The annals of Mathematics, 63,

, 308--323.

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Published

2019-09-20

Issue

Vol. 38 No. 2 (2019): :

Section

Articles

How to Cite

ON HOLOMORPHY OF FENYVES BCI-ALGEBRAS. (2019). Journal of the Nigerian Mathematical Society, 38(2), 139-155. https://ojs.ictp.it/jnms/index.php/jnms/article/view/469