IJPAM: Volume 60, No. 1 (2010)
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, P.R. CHINA
e-mail: kong_fd@yahoo.cn
Abstract.As a proper generalization
of Goldie extending module, we introduce the concept of weakly
-extending module. Let
. Then
if
and only if there exist submodules
and
of
such that
,
and
.
is called a weakly
-extending module if for every submodule
of
,
there exists a direct summand
of
such that
. Let
, where
and
are weakly
-extending. It is shown that if
is
-ejective
(or
is
-ejective), then
is weakly
-extending. Finally, we show that if
is weakly
-extending, then so is its rational hull.
Received: September 19, 2009
AMS Subject Classification: 16D70
Key Words and Phrases: extending module, -extending module, weakly
-extending module
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1