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The primary purpose of this research article is to study the famous Kothe's Conjecture for the special cases - when a ring R is commutative, and when R is an Algebra over a field. Furthermore, some open problems involving tensor product of Algebras over a field has also been discussed extensively along with their proofs. Subsequently, an equivelent statement of Kothe's problem in terms of algebra of matrices has been established.
Subham De (Mon,) studied this question.