| Popis: |
Let GG be a group and RR be a GG-graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal. A proper graded ideal PP of RR is said to be a graded weakly 1-absorbing primary ideal of RR if whenever nonunit elements x,y,z∈h(R)x,y,z\in h\left(R) such that 0≠xyz∈P0\ne xyz\in P, then xy∈Pxy\in P or zn∈P{z}^{n}\in P, for some n∈Nn\in {\mathbb{N}}. Several properties of graded weakly 1-absorbing primary ideals are investigated. |
