الفهرس 
Chapter 1: Basic concepts and resultsOnly 14 pages are availabe for public view
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Abstract
In 1966, Y. Imai and K. Isèki introduced two classes of abstract algebras: BCK-algebras
and BCI-algebras [27, 28, 29, 30, 31, 32]. It is known that the class of BCK-algebras is proper
subclass of the class of BCI-algebras. J. Neggers, et al. [55] introduced a notion, called Qalgebras,
which is a generalization of BCH / BCI / BCK-algebras and generalized some
theorems discussed in BCI-algebras. Moreover, Ahn and Kim [3] introduced the notion of
QS-algebras which is a proper subclass of Q-algebras. Kondo [39] proved that, each theorem
of QS-algebras is provable in the theory of abelian groups and conversely each theorem of
abelian groups is provable in the theory of QS-algebras. In [17], W. A. Dudek and X. H.
Zhang introduced a new notion of ideals in BCC-algebras and described connections between
such ideals and congruences.
In the theory of rings, the properties of derivations are important. The notion of the ring
with derivation is quite old and plays a significant role in the integration of analysis,
algebraic geometry and algebra. Several authors [5, 6, 9, 10, 36, 37, 41] have studied
derivations in rings and near rings. Jun and Xin [35] applied the notion of derivations in ring
and near-ring theory to BCI-algebras, and they also introduced a new concept called a
regular derivation in BCI -algebras.
They investigated some of its properties, defined a d -derivation ideal and gave conditions
for an ideal to be d-derivation. Later, Abujabal and Al-Shehri [2], defined a left derivation in
BCI-algebras and investigated a regular left derivation. Zhan and Liu [65] studied fderivations
in BCI-algebras and proved some results.
Muhiuddin and Al-roqi [53] introduced the notion of ) , ( -derivation in a BCI-algebra
and investigated related properties. They provided a condition for a ( , ) - derivation to be
regular. They also introduced the concepts of a ( , ) d - invariant ( , ) -derivation and α-
ideal, and then they investigated their relations. Furthermore, they obtained some results on
regular ( , ) -derivations. Moreover, they studied the notion of t-derivations on BCIalgebras
[54] and obtain some of its related properties. Further, they characterize the notion
of p-semisimple BCI-algebra X by using the notion of t-derivation. C.Prabpayak
,U.Leerawat [57] applied the notion of a regular derivation to BCC-algebras and investigated
some related properties