In this paper there is proposed a method of partition the attributes of relation scheme in equivalence classes and in nonre-dundant equivalence classes. Several properties of these equivalence classes are proved. Their properties serve as the basis for an algorithm with a polynomial complexity, which determines the prime attributes of a database schema.
In this paper, based on equivalence classes of attributes there are formulated necessary and sufficient conditions that constraint a database schema to be in the second, third or Boyce-Codd normal forms. These conditions offer a polynomial complexity for the testing algorithms of the normalizations level.