  We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$
transfer matrices, for both closed and open spin chains. We use these
relations, which we call factorization identities, to solve the models by
algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like
open spin chain with an even number of sites that depends on a continuous
parameter, which we interpret as the rapidity of the boundary.
