Two inequalities for parameters of a cellular algebra

Two inequalities are proved. The first one generalizes for cellular algebras a well-known theorem about coincidence of the degree and the multiplicity of an irreducible representation of a finite group in the regular representation of it. The second inequality which is proved for primitive cellular algebras, gives an upper bound for the minimum subdegree of a primitive permutation group in terms of the degrees of its irreducible representations in the permuation representation.