Abstract
A decomposition of an R-module into submodulesM = +M α, is called deep if for every submodule H of M, we have H = +(H ∩ M α). We characterize when deep decompositions exist. We then show that M ≃ +MP (over all maximal ideals P) if and only if R/(Ann m) is a finite direct sum of quasi-local rings for all 0 ≠ m ∈ M. We also show this decomposition is deep.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
