Baneen Najah Abbas Al-kuzaa

In this research we have introduced the concept of fuzzy AB-ideal of AB-algebra and also we proved some relevant characteristics and theories. We also studied the fuzzy relations on AB-algebras and fuzzy derivations AB-ideals. We presented the characteristics and theories that illustrat the two concepts that is promted us to study Cartesian Product of fuzzy derivations AB-ideals

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

The aim of this paper is to introduce and study new algebraic structure, called AB-algebra and investigate some of its properties. We give the notion of AB-ideal of AB-algebra and quotient AB-Algebras, several theorems, properties are stated and proved.

With technological development, hackers are possible to access the transmitted data, so we need to constantly develop encryption methods to increase security. In this paper, we have introduced a new cryptosystem hexadecnion polynomial RSA (PH-RSA) by mixing NTRU and polynomial RSA based on a hexadecnion polynomial instead of polynomial RSA with a high level of security.