Idempotent Computation over Finite Fields

In this paper, we provide an account of several new techniques for computing the primitive idempotents of a commutativeartinian algebra over a finite field. Examples of such algebras include the center of a finite group algebra or any finite dimensional quotient of a polynomial ring. The computational methods described are applicable in fairly general situations and the algorithms presented are easily programmed. Both pseudocode and operation counts are provided. As an application, the problem of factoring polynomials over finite fields is discussed.