Identities with Kinds of Derivations in Rings : Center-Like Subsets, Generalized Derivations With Hochschild 2-Cocycles, Centrally-Extended Generalized -Derivations

ISBN-13: 9786200095336 / Angielski

Mohammad Nagy Daif; Osama Hamed Ezzat; Hesham Nabiel

Opis

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(x y))^m= (x y)^n.

O autorze

Nagy Daif, Mohammad
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.