
Vietnam Journal of Mathematics 35:2(2007)
215222

HCofinitely Supplemented Modules

Muhammet Tamer
Kosan

Abstract. Let M be a right Rmodule.
We call M Hcofinitely 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 Hcofinitely
supplemented Duo module. Then every direct summand of M is Hcofinitely
supplemented module. (2) Let be a Duo module. If M_{1} and M_{2}
are Hcofinitely supplemented
modules, then M is Hcofinitely supplemented. (3)
Assume Rad(M) << M. Then M is Hcofinitely
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 Rmodule. M is Hcofinitely supplemented if and only if every maximal
submodule of M has an Hsupplement in M.

2000 Mathematics Subject Classification: 16D99.

Keywords: Duo modules, Hsupplemented modules, Hcofinitely
supplemented modules.


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