IJPAM: Volume 21, No. 1 (2005)

FINITELY $\oplus-$SUPPLEMENTED MODULES

Hamza Çalisici$^1$, Ali Pancar$^2$
$^1$Department of Mathematics
Faculty of Education
Ondokuz Mayis University
Amasya, 05189, TURKEY
e-mail: hcalisici@omu.edu.tr
$^2$Department of Mathematics
Faculty of Arts and Sciences
Ondokuz Mayis University
Samsun, 55139, TURKEY
e-mail: apancar@omu.edu.tr


Abstract.Let $R$ be a ring and $M$ a left $R$-module. $M$ is called finitely H-supplemented if for every finitely generated submodule $N$ of $M$, there exists a direct summand $L$ of $M$ such that $M = N + X$ holds if and only if $M = L + X$. $M$ is called finitely $\oplus-$supplemented if every finitely generated submodule $N$ of $M$ has a supplement that is a direct summand of $M$. In this paper various properties of these modules are given. It is shown that a ring $R$ is finitely semiperfect if and only if every finitely generated free $R$-module is finitely $\oplus-$supplemented.

Received: March 23, 2005

AMS Subject Classification: 16D99

Key Words and Phrases: semiperfect ring, supplement submodule, finitely $\oplus-$ supplemented module

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 1