Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5589
Title: Coneat submodules and coneat-flat modules
Authors: Büyükaşık, Engin
Durgun, Yılmaz
Keywords: Absolutely neat module
Coclosed submodule
Coneat submodule
Publisher: Korean Mathematical Society
Source: Büyükaşık, E., and Durğun, Y. (2014). Coneat submodules and coneat-flat modules. Journal of the Korean Mathematical Society, 51(6), 1305-1319. doi:10.4134/JKMS.2014.51.6.1305
Abstract: A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism N → S can be extended to a homomorphism M → S. M is called coneat-flat if the kernel of any epimorphism Y → M → 0 is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneatflat if and only if M+ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m- injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.
URI: https://doi.org/10.4134/JKMS.2014.51.6.1305
http://hdl.handle.net/11147/5589
ISSN: 0304-9914
0304-9914
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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