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Vietnam Journal of Mathematics 35:2(2007) 215-222

 H-Cofinitely Supplemented Modules

Muhammet Tamer Kosan

Abstract.  Let M be a right R-module. We call M H-cofinitely supplemented if for very cofinite submodule A of M (i.e. the factor module M/A is finitely generated) there exists a direct summand D of M such that M = A + X holds if and only if M = D + X. It is shown that in this paper: (1) Let M be an H-cofinitely supplemented Duo module. Then every direct summand of M is H-cofinitely supplemented module. (2) Let be a Duo module. If M₁ and M₂ are H-cofinitely supplemented modules, then M is H-cofinitely supplemented. (3) Assume Rad(M) << M. Then M is H-cofinitely supplemented if and only if every cofinite submodule of M/Rad(M) is direct summand and each cofinite direct summand of M/Rad(M) lifts to a direct summand of M. In addition, let M be a duo right R-module. M is H-cofinitely supplemented if and only if every maximal submodule of M has an H-supplement in M.

2000 Mathematics Subject Classification: 16D99.

Keywords: Duo modules, H-supplemented modules, H-cofinitely supplemented modules.

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