2006/12/23 by Futoshi Hayasaka, Hayasaka, Futoshi
Computer Science · Mathematics · #13D05 #13H05 #13H10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13D05 #msc:13H05 #msc:13H10
paper · pdf · doi:10.48550/arxiv.math/0612741
15 pages
arxiv created 2006/12/23 · openalex publication_date 2006/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (A, m) be a Noetherian local ring and N a parameter module in F=Ar and M=N:F m the socle module of N. In this paper, we shall prove that the module M=N:F m has a reduction number at most one and hence its Rees algebra R(M) is Cohen-Macaulay, if the base ring A is Cohen-Macaulay of dimension two and the rank of N is greater than or equal to two. This result gives numerous examples of Cohen-Macaulay Rees algebras of modules, which are not integrally closed and not a parameter module.