Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6760
Title: Co-coatomically supplemented modules
Authors: Alizade, Rafail
Güngör, Serpil
Keywords: Modules (Algebra)
Dedekind domain
Supplement submodule
Issue Date: Dec-2017
Publisher: Springer Verlag
Source: Alizade, R., and Güngör, S. (2017). Co-coatomically supplemented modules. Ukrainian Mathematical Journal, 69(7), 1007-1018. doi:10.1007/s11253-017-1411-x
Abstract: It is shown that if a submodule N of M is co-coatomically supplemented and M/N has no maximal submodule, then M is a co-coatomically supplemented module. If a module M is co-coatomically supplemented, then every finitely M-generated module is a co-coatomically supplemented module. Every left R-module is co-coatomically supplemented if and only if the ring R is left perfect. Over a discrete valuation ring, a module M is co-coatomically supplemented if and only if the basic submodule of M is coatomic. Over a nonlocal Dedekind domain, if the torsion part T(M) of a reduced module M has a weak supplement in M, then M is co-coatomically supplemented if and only if M/T (M) is divisible and TP (M) is bounded for each maximal ideal P. Over a nonlocal Dedekind domain, if a reduced module M is co-coatomically amply supplemented, then M/T (M) is divisible and TP (M) is bounded for each maximal ideal P. Conversely, if M/T (M) is divisible and TP (M) is bounded for each maximal ideal P, then M is a co-coatomically supplemented module.
URI: http://doi.org/10.1007/s11253-017-1411-x
http://hdl.handle.net/11147/6760
ISSN: 0041-5995
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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