A Note On Ideals Of a Three-Dimenensional Associative Algebra

In this paper,we shall apply the theory of nilpotent radical toderive Some results about ideals of a three-dimensional associatvealgebra over a field F and of an associative ring of order P^3 where Pis a prime.These results are useful in studying the structure of thealgebra and the ring. THEOREM 1.Let A be a three-dimensional associative algebraover a field F,N(A)the nilpotent radical of A.If N(A)≠O。