Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 3
A variation of supplemented modules
- Pages
- 418–426
- DOI
- —
Abstract
Over a general ring, an R-module is w-supplemented if and only if amply w-supplemented. It is proved that over a local Dedekind domain, all modules are w-supplemented and over a non-local Dedekind domain, an R-module M is w-supplemented if and only if Soc(M)\ll M or M=S0 \oplus (\bigoplusi \in I K), where S0 is a torsion, semisimple submodule of M and K is the field of quotients of R.
Özet
Over a general ring, an R-module is w-supplemented if and only if amply w-supplemented. It is proved that over a local Dedekind domain, all modules are w-supplemented and over a non-local Dedekind domain, an R-module M is w-supplemented if and only if Soc(M)\ll M or M=S0 \oplus (\bigoplusi \in I K), where S0 is a torsion, semisimple submodule of M and K is the field of quotients of R.