Graded weakly 1-absorbing primary ideals

Abstract

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.

Keywords

• graded prime ideal
• graded weakly prime ideal
• graded primary ideal
• graded weakly primary ideal
• graded 2-absorbing primary ideal
• graded weakly 2-absorbing primary ideal
• graded 2-absorbing ideal
• graded weakly 2-absorbing ideal
• graded n-absorbing ideal
• 13a02
• 13a15
• 16w50