Some Studies on Left Generalized Derivations in Rings

In the theory of derivation rings, the study of associative rings has evoked great interest and assumed importance.The notation of rings with derivations plays a significant role in the integration of analysis, algebraic geometry and algebra.The theory of derivations plays an important role in quantum physics. The study of bounded derivations on operator algebras started in 1950s and has been very actively carried out by many mathematicians, and it has become a useful mathematical theory.After the study of bounded derivations,the study of unbounded derivations is being carried on by many mathematicians and mathematical physicists,and this theory is making great progress.The study of derivation rings is bound to be useful,for it is a valuable tool in areas of Mathematics such as Graph theory,Functional analysis as well as in more practical world of Mathematical Economics,Computer Science and Engineering.