Finite Codimensional Ideal And Finite Type Module Of Quantum Algebras

The quantum algebra is an algebra with generators and relations. Let A = Z[v]_m, where v is an indeterminate and m is an ideal in Z[v] generated by v-1 and a fixed odd prime p, A'=Q(v) is the fraction field of A, let U' is a quantum algebra over A' associated to Car tan matrix (a_ij)_n×n, U is a quantum algebra over A. In this paper gives several features of weight space of finite type module of quantum algebra, and discusses some relationship between the two finite codimensional ideals of quantum algebra U mentioned in [1] and [6].