On graded radical ideals of graded non-commutative rings
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Let $G$ be a group and $R$ a $G$-graded ring$.$ In 2023, Al-Shorman et al. introduced the concept of graded $J$-ideals of a $G$ -graded commutative ring and several characterizations of this concept were investigated. The notion of gr-$n$-ideals in a $G$-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 $G$-graded rings as a special case.
Abstract
Let $G$ be a group and $R$ a $G$-graded ring$.$ In 2023, Al-Shorman et al. introduced the concept of graded $J$-ideals of a $G$ -graded commutative ring and several characterizations of this concept were investigated. The notion of gr-$n$-ideals in a $G$-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 $G$-graded rings as a special case.
참고문헌 (11)
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