Let G be a group with identity e and R be G-graded commutative ring with \(1 \ne 0\) . In this paper, we study two generalizations of a graded prime ideal. A proper ideal I of R is called a graded n-absorbing (resp., graded strongly n-absorbing) ideal if whenever \(x_1 \cdots x_{n+1} \in I\) for \(x_1, \ldots , x_{n+1} \in h(R)\) (resp., \(I_1 \cdots I_{n+1} \subseteq I\) for graded ideals \(I_1, \ldots , I_{n+1}\) of R ), then there are n of the \(x_i\) ’s (resp., n of the \(I_i\) ’s) whose product is in I. We give some properties and characterizations of these graded ideals in several classes of graded commutative rings, and we wonder when these two concepts are equivalent. Our results provide new techniques for constructing new original examples that satisfy the above properties.
