  Bell and Zhang have shown that if $A$ and $B$ are two connected graded
algebras finitely generated in degree one that are isomorphic as ungraded
algebras, then they are isomorphic as graded algebras. We exploit this result
to solve the isomorphism problem in the cases of quantum affine spaces, quantum
matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our
result involves determining the degree one normal elements, factoring out, and
then repeating. This creates an iterative process that allows one to determine
relationships between relative parameters.
