Let be a finite set of endomorphisms of a finite dimension vector space Kⁿ over a field K. We prove that if φ is a product φ₁φ₂ ··· φ_m of endomorphisms of Kⁿ belonging to , we can extract of it a product φ_iφ_{i + 1} ··· φ_j = ψ which is a pseudoregular endomorphism. That is: ψ has a representation as a square matrix over K which is diagonal sum of a null matrix and of a regular one. This result holds also if K is a skew-field. As a consequence of this result, we obtain two theorems about the rational power series in noncommuting variables. The first concerns the “regularity” of the support of the rational power series. The second generalizes a theorem of Polyà [12] and another one of Cantor [2], about rational power series with algebraic integer coefficients.