2013/08/29 by Saeed Jahandoust, Jahandoust, Saeed, Reza Naghipour +1
Computer Science · Mathematics · #13B2 #13B22 #13E05 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13B2 #msc:13B22 #msc:13E05
paper · pdf · doi:10.48550/arxiv.1308.6449
5 pages, to appear in Journal of Pure and Applied Algebra
arxiv created 2013/08/29 · openalex publication_date 2013/08/29 · arxiv updated 2013/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R denote a commutative Noetherian ring, I an ideal of R, and let S be a multiplicatively closed subset of R. In \citeRa1, Ratliff showed that the sequence of sets \rm AssRR/I⊆ \rm AssRR/I2 ⊆ \rm AssR R/I3⊆ … increases and eventually stabilizes to a set denoted A^∗(I). In \citeMc2, S. McAdam gave an interesting description of A^∗(I) by making use of R[It,t-1], the Rees ring of I. In this paper, we give a second description of A^∗(I) by making use of the Rees valuation rings of I. We also reprove a result concerning when InRS∩ R=In for all integers n>0.