IJPAM: Volume 80, No. 5 (2012)

TOTALLY COFINITELY WEAK
RAD-SUPPLEMENTED MODULES

Figen Yüzbaşi Eryilmaz, Şenol Eren
Deparment of Mathematics
Faculty of Sciences and Arts
Ondokuz Mayıs University
55139, Kurupelit, Samsun, TURKEY


Abstract. Let $R$ be a ring and $M$ be a left $R-$module. $M$ is called cofinitely weak Rad-supplemented if every cofinite submodule of $M$ has a weak Rad-supplement in $M$. In this paper, we will define totally cofinitely weak Rad-supplemented modules. In general, the finite sum of totally cofinitely weak Rad-supplemented modules need not to be totally cofinitely weak Rad-supplemented. However a module totally cofinitely weak Rad-supplemented if and only if it is the direct sum of a semisimple module and a totally cofinitely weak Rad-supplemented module. We will prove a module $M$ is totally cofinitely weak Rad-supplemented if and only if $\frac{%
M}{K}$ is totally cofinitely weak Rad-supplemented for a linearly compact submodule $K$ of $M$. Similarly, a module $M$ is totally cofinitely weak Rad-supplemented if and only if $\frac{M}{U}$ is totally cofinitely weak Rad-supplemented for a uniserial submodule $U$ of $M$.

Received: August 8, 2012

AMS Subject Classification: 16D10, 16L30, 16D99

Key Words and Phrases: cofinite submodule, cofinitely weak rad-supplemented module, totally cofinitely weak rad-supplemented module

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 5