2013/08/28 by Saeed Jahandoust, Jahandoust, Saeed, Reza Naghipour +1
Mathematics · #13B2 #13B22 #13E05 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13B2 #msc:13B22 #msc:13E05
paper · pdf · doi:10.48550/arxiv.1308.6048
15 pages
arxiv created 2013/08/28 · openalex publication_date 2013/08/28 · arxiv updated 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let I denote an ideal of a Noetherian ring R. The purpose of this article is to introduce the concepts of quintasymptotic sequences over I and quintasymptotic cograde of I, and it is shown that they play a role analogous to quintessential sequences over I and quintessential cograde of I, given in \citeRa1. Also, we show that, if R is local, then the quintasymptotic cograde of I is unambiguously defined and behaves well when passing to certain related local rings. Finally, we use this cograde to characterize of two classes of local rings.