Modules of reduction number one
Abstract
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.
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