ON GRADED RADICAL IDEALS OF GRADED NON-COMMUTATIVE RINGS

. Let C be a group and R a C-graded ring. In 2023, AlShorman et al. introduced the concept of graded J-ideals of a C-graded commutative ring and several characterizations of this concept were investigated. The notion of gr-n-ideals in a C-graded commutative ring was introduced by Al-Zoubi et al. and studied. In this note, we introduce the concept of a graded rho-ideal (gr-rho-ideal) for a graded special radical rho G and show that the results of graded J-ideals and graded n-ideals are special cases of a more general situation. We prove that most of the results in graded commutative rings of the above-mentioned papers are satisfied for non-commutative C-graded rings as a special case.