On Some Special Cases of K ¨othe’s Conjecture

The primary purpose of this research article is to study the famous Köthe'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 Köthe's problem in terms of algebra of matrices has been established.