الفهرس 
Chapter one:Basic concepts and resultsOnly 14 pages are availabe for public view
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Abstract
As it is well known, BCK and BCI-algebras are two classes of algebras of logic. They were introduced by Imai and Iseki [21, 22,26 ] and have been extensively investigated by many researchers. It is known that the class of BCK-algebras is a proper sub class of the BCI-algebras. The essential difference between BCK-algebras and BCI-algebras lies in the following: The Element 0 is the least element in BCK-algebras, while it is a minimal element in BCIalgebras .The class of all BCK-algebras is a quasivariety. Is´eki posed an interesting problem (solved by Wro´nski [ 58]) whether the class of BCK-algebras is a variety. In connection with this problem, Komori [37 ] introduced a notion of BCC-algebras, and Dudek [ 15] redefined the notion of BCC-algebras by using a dual form of the ordinary definition in the sense of Komori. Dudek and Zhang [16 ] introduced a new notion of ideals in BCC-algebras and described connections between such ideals and congruences .