Bøger af Areej Tawfeeq Hameed

This Book consists of five chapters. We introduce a new notion of algebras called AT-algebras. The notions of AT-algebras, AT-subalgebras, AT-ideals and homomorphism of AT-algebras are introduced. The relation between some abelian groups and AT-algebras are studied and investigated some of its properties . We introduce the notion of fuzzy AT-ideal of AT-algebra, several theorems, properties are stated and proved. the notion of interval-valued fuzzy AT-subalgebras and interval-valued fuzzy AT-ideals on AT-algebras is introduced. We introduced a new notion called cubic AT-ideal of AT-algebras and study several properties of it. we discuss fuzzy ¿-translation, (normalized, maximal) fuzzy S-extension of fuzzy AT-subalgebras in AT-algebra.We discuss fuzzy ¿-translation, fuzzy extension of fuzzy AT-ideals in AT-algebra. We studied and investigated some of its properties.

In this book, we introduce a new notion of algebras called KUS-algebras. The notions of KUS-algebras, KUS-subalgebras, KUS-ideals and homomorphism of KUS-algebras are introduced. We introduce the notion of fuzzy KUS-ideal of KUS-algebra, several theorems, properties are stated and proved. The notion of interval-valued fuzzy KUS-ideals on KUS-algebras is introduced. Several theorems of i-v fuzzy KUS-ideal are stated and proved. We introduce the notion of anti-fuzzy KUS-ideals of KUS-algebras and we will introduce a new notion called cubic KUS-ideal of KUS-algebras and study several properties of its. We discuss fuzzy ¿-translation (fuzzy ¿-multiplication) , (normalized, maximal) fuzzy S-extension of fuzzy KUS-subalgebras on KUS-algebra and fuzzy KUS-ideals on KUS-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