On Almost Quasi-Frobenius Fuzzy Rings

In this book we introduce almost quasi-Frobenius fuzzy ring of a ring by extending the notion of (ordinary) quasi-Frobenius rings. The book consists of three chapters. Chapter one reviewed some basic definitions and results. Chapter two we introduce the notion of an Annihilator of a fuzzy ideal of a ring by extending the notion of (ordinary) annihilator of an ideal of a ring. We also state and prove some basic results about this concept. We introduce the notion of an Annihilator fuzzy ideal of a ring by extending the notion of (ordinary) annihilator ideal of a ring. We study and give some properties of the concept and we introduce the notion of a fuzzy external direct sum of fuzzy rings. We study and give some properties of the concept. Among other results. In Chapter three we the notion of an almost quasi-Frobenius fuzzy ring. We give some examples to explain this concept and give some characterizations of it. And we introduce the notion of principal ideal fuzzy ring and recall the definition of Boolean fuzzy ring. Also we study the relationships between these concepts and almost quasi-Frobenius fuzzy rings.