Beschreibung
The main object of the book is to study specific classes of rings satisfying certain kinds of identities involving several types of derivations. It falls in seven chapters. Chapter 1 is focused on mentioning main definitions and concepts that will be used in the book. Chapter 2 considers specific subsets defined by some conditions which are proved to coincide with the center Z for certain classes of rings endowed with kinds of maps. Chapter 3 is devoted to studying the relationship between generalized derivations associated with Hochschild 2-cocycles and generalized Jordan triple derivations associated with Hochschild 2-cocycles. The contents of Chapter 4 are motivated by a recent work due to Bell and Daif in 2016 who introduced the concept of centrally-extended derivations and centrally-extended endomorphisms on rings. Chapter 5 studies some classes of *-rings admitting various types of *-maps. Chapter 6 continues the studying of some types of mappings f satisfying the identity f^2(x) = x where x is an element in a specific subset of the ring. Involutions are much studied examples. Chapter 7 discusses the commutativity of a prime ring satisfies the identity (F(xy))^m= (xy)^n.
Autorenporträt
Mohammad Nagy Daif, Professor of Mathematics, Al-Azhar University, Cairo, Egypt;Osama Hamed Ezzat, Lecturer of Mathematics, Al-Azhar University, Cairo, Egypt;Hesham Nabiel, Lecturer of Mathematics, Al-Azhar University, Cairo, Egypt.
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