Graded divided ideals in a graded integral domain

Let [Formula: see text] be a commutative integral domain graded by an arbitrary torsionless monoid [Formula: see text]. In this paper, we present the concept of graded divided ideals in graded integral domains, expanding the understanding of divided ideals in ungraded context. It delves into the fundamental properties of these ideals, illustrating their distinctions from the ungraded counterpart and investigating their properties. Moreover, we introduce and study a generalization of divided domains to the context of integral domains graded by a torsionless monoid.