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arXiv · 1812.06541

G-graded irreducibility and the index of reducibility

Cheng Meng
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Abstract

Let $R$ be a commutative Noetherian ring graded by a torsionfree abelian group $G$. We introduce the notion of $G$-graded irreducibility and prove that $G$-graded irreducibility is equivalent to irreducibility in the usual sense. This is a generalization of Chen and Kim's result in the $\mathbb{Z}$-graded case. We also discuss the concept of the index of reducibility and give an inequality for the indices of reducibility between any radical non-graded ideal and its largest graded subideal.

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Cheng Meng. 2018-12-16. G-graded irreducibility and the index of reducibility. https://arxiv.org/abs/1812.06541

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