  Some filtrations of the tensor product of a highest weight module and a
lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in
\cite{LZ:2009} and one can use them to define some ideals of the modified
quantized enveloping algebra. It is shown that the quotient algebras inherit
canonical bases from the modified quantized enveloping algebra and are dual to
the quantum coordinate ring defined by Kashiwara for symmetrizable Kac-Moody
algebra $\mathfrak g$.
