Graded uniformly \(n\)-ideals of commutative rings (Q6579988)

Let \(G\) be a group with identity \(e.\) Let \(R\) be a \(G\)-graded commutative ring. In this paper, author has introduced and studied the concept of graded uniformly \(n\)-ideal(in short, gr-u-\(n\)-ideal). Many results concerning gr-u-\(n\)-ideals are obtained. In particular, it is proved that for a \(G\)-Noetherian ring \(R,\) the following are equivalent:\N\N(1) Every graded ideal of R is a gr-u-\(n\)-ideal;\N\N(2) Every gr-prime ideal is a gr-u-\(n\)-ideal;\N\N(3) R is a G-graded local ring with a gr-maximal ideal that is graded nil ideal.