Derivation of AB-ideals and fuzzy AB-ideals of AB-algebra

In this book,we introduce a new concept and generalization of BCC-algebra, which we have called it AB-algebra. We have proved the truth of the definition through the examples exist. We have that confirmed by a computer program at the end existing of the thesis with appendices. That led us to view the concepts related to them, subalgebras and ideals and the fuzzy of them for AB-algebras. We have also proved some important propositions and theorems relevant to the subject They which explain specific cases. We have studied the converse of some theorems to be sure whether they are correct or not . On the other hand, we study the weak AB-algebra and we proved some results of it. We introduce the concept of homomorphism for the ideal of AB-algebra and its fuzzy that is related to an AB-algebra. We have also to studied the normal fuzzy AB-algebra and some characteristics and result of it. Finally, we introduce the concept of derivations and fuzzy derivations relative to AB-algebra and proved some results and properties relevant to the same subject. Porf. Dr. Areej Tawfeeq Hameed