2018/12/16 by Cheng Meng, Meng, Cheng · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1812.06541
openalex publication_date 2018/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.