2016/12/22 by Nguyen Tu Cuong, Cuong, Nguyen Tu, Phạm Hùng Quý +1
Mathematics · #13D45 #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1612.07638
openalex publication_date 2016/12/22 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
Let (R, \frak m) be a homomorphic image of a Cohen-Macaulay local ring and M a finitely generated R-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show that every finitely generated R-module M is associated by a sequence of invariant modules. This modules sequence expresses the deviation of M with the Cohen-Macaulay property. This result generalizes the unmixed theorem of Cohen-Macaulayness for any finitely generated R-module. As an application we construct a new extended degree in sense of Vasconcelos.