IJPAM: Volume 80, No. 5 (2012)
RAD-SUPPLEMENTED MODULES
Deparment of Mathematics
Faculty of Sciences and Arts
Ondokuz Mayıs University
55139, Kurupelit, Samsun, TURKEY
Abstract. Let be a ring and
be a left
module.
is called cofinitely weak Rad-supplemented if every cofinite submodule of
has a weak Rad-supplement in
. 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
is totally cofinitely weak Rad-supplemented if and only if
is totally cofinitely weak Rad-supplemented for a linearly compact
submodule
of
. Similarly, a module
is totally cofinitely weak
Rad-supplemented if and only if
is totally cofinitely weak
Rad-supplemented for a uniserial submodule
of
.
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
Download paper from here.
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