Superposition principle in Algebraic quantum theory

The generalized superposition principle for the states over observable algebras proposed by V. N. Sushko and the author, is thoroughly analysed. It is proved, in particular, that the generalized superposition of pure vector states is determined uniquely, up to the relative phase. Comparison with other algebraic formulations of the superposition principle as well as with the treatment of this principle in the quantum logic approach is made.