  A scheme based on a unifying q-deformed algebra and associated with a
generalized Lax operator is proposed for generating integrable quantum and
statistical models. As important applications we derive known as well as novel
quantum models and obtain new series of vertex models related to q-spin,
q-boson and their hybrid combinations. Generic q, q roots of unity and q -> 1
yield different classes of integrable models. Exact solutions through algebraic
Bethe ansatz is formulated for all models in a unified way.
