Sequential 1-Cohen-Macaulayness for direct sums of modules

Mathematics > Commutative Algebra [Submitted on 16 Jun 2026] Title:Sequential 1-Cohen-Macaulayness for direct sums of modules View PDF HTML (experimental)Abstract:Let (R,m) be a Noetherian local ring and M1,...,Mn finitely generated R-modules. Set M is the direct sum of Mi. The main purpose of this paper is to extend the results on the sequential Cohen-Macaulayness of the direct sum of modules (Taniguchi et al, 2018), the sequential generalized Cohen-Macaulayness of the direct sum of modules (Cuong and Nhan, 2003) We first describe the largest submodule of M of dimension less than dimM by using the largest submodule so f its component modules. Then we give a necessary and sufficient condition for M being 1-Cohen-Macaulay. The purpose of this paper is to characterize the sequential 1-Cohen-Macaulayness of the direct sum M. We show that M is sequentially 1-Cohen-Macaulay if and only if Mi is sequentially 1-Cohen-Macaulay for all i <=n. We provide an example to clarify the results. We employ inductive methods as well as the dimension filtration of a finitely generated module. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.