Some remarks concerning Demazure’s construction of normal graded rings

In 1, Demazure showed a new way of constructing normal graded rings using the concept of “rational coefficient Weil divisors” of normal projective varieties and he showed, among other things, the following THEOREM (1, 3.5). If R = ⊕ n ≥ 0 R n is a normal graded ring of finite type over a field k and if T is a homogeneous element of degree 1 in the quotient field of R, then there exists unique divisor D ∈ Div ( X , Q ) ( X = Proj ( R )), such that for every n ≧ 0.( See (1.1) for the definition of