CONEAT SUBMODULES AND CONEAT-FLAT MODULES


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Buyukasik E. , Durgun Y.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.51, ss.1305-1319, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 6
  • Basım Tarihi: 2014
  • Doi Numarası: 10.4134/jkms.2014.51.6.1305
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.1305-1319

Özet

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 coneat-flat 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 fiat modules coincide.