Homogeneous splitting sets of a graded integral domain

Let R=⊕α∈ΓRα be a graded integral domain, and let H be the set of nonzero homogeneous elements of R. In this paper, we study when H is a (t-)splitting set of R and the saturated multiplicative subsets S of R such that H=ST, where T={t∈H|(s,t)v=R for all s∈S}.