IJPAM: Volume 53, No. 2 (2009)

ON COFINITELY RAD-SUPPLEMENTED MODULES

Ergül Türkmen$^1$, Ali Pancar$^2$
$^{1,2}$Department of Mathematics
Faculty of Arts and Sciences
Ondokuz Mayis University
Samsun, 55139, TURKEY
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Let $R$ be a ring and $M$ be a left $R-$module. In this work some properties of (amply) cofinitely $\text{\rm Rad}$-supplemented modules are developed. It is shown that if $M$ contains a nonzero semi-hollow submodule then $M$ is cofinitely $\text{\rm Rad}$-supplemented if and only if $M/N$ is cofinitely $\text{\rm Rad}$-supplemented. Morever a module $M$ with small radical is cofinitely $\text{\rm Rad}$-supplemented such that $\text{\rm Rad}$-supplements are supplements in $M$, then $M$ is cofinitely supplemented. In addition, a ring $R$ is left $\text{\rm Rad}$-supplemented if and only if every left $R$-module is amply cofinitely $\text{\rm Rad}$-supplemented. Also, we give a characterization of generalized semiperfect modules.

Received: February 27, 2009

AMS Subject Classification: 16D10, 16D99

Key Words and Phrases: cofinite submodule, $\text{\rm Rad}$-supplement, (amply) cofinitely $\text{\rm Rad}$-supplemented module, generalized projective cover

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2