Generalized transforms of graded Strong Mori domains

Abstract

Let Γ be a torsion-free cancellative monoid and let R = ⊕ α ∈ Γ R α be a graded integral domain. In this paper, we show that if R is a graded Strong Mori domain, then every homogeneously t-linked overring of R contained in R hwg is a graded Strong Mori domain, where Rhwg is the homogeneous w-global transform of R; and if R is a graded Strong Mori domain, then R S is also a graded Strong Mori domain, where S is a multiplicative set of ideals of R generated by homogeneous ideals of R.