An algebraic form of the factorization method

The Infeld-Hull factorization method is recast in more general algebraic form which may be looked at as the most natural extension of the oscillator algebra. Nonrelativistic and relativistic hydrogen problems appear simpler and perfectly analogous, whereby the factors in both cases are directly related to the characteristic hidden symmetries. Close connections to nonlinear problems and more general algebraic properties yield relations to recent developments.