The Necessary and Sufficient Condition on Which the R-classical Linear Lie Algebra is R-simple Lie Algebra

Because the classical linear Lie algebra over a field is a simple Lie algebra,but the classical linear Lie algebra over a ring with identity may not still be a simple Lie algebra,and the classification and structure of simple Lie algebras is critical to the study of the the structure and classification of the semi-simple Lie algebra,even solvable,nilpotent Lie algebra,here we give the necessary and sufficient condition on which the R-classical linear Lie algebra is R-simple Lie algebra.