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The scope of this research algebra book is intended for a highly completed knowledge in the topic of commutativity of associative rings with ordinary derivations. The study of this theme has been begun in 1957 by Posner and has been followed by many authors through studying different algebraic conditions. This book contains six chapters. Chapter one is devoted to review briefly the terminology and the technical language that are basic to the understanding of the book. Chapter two deals with second classical theorem of Posner on prime rings with derivations and its diverse generalizations....