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Rings whose modules are direct sums of extending modules
Author(s):
Noyan
Er
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2265-2271.
MSC (2000):
Primary 16D10, 16D70, 16P20;
Secondary 16G60
Posted:
January 30, 2009
MathSciNet review:
2495259
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Abstract:
We prove that for a ring  , the following are equivalent: (i) Every right  -module is a direct sum of extending modules, and (ii)  has finite type and right colocal type (i.e., every indecomposable right  -module has simple socle). Thus, in this case,  is two-sided Artinian and right serial, and every right  -module is a direct sum of finitely generated uniform modules. This property of a ring is not left-right symmetric. A consequence is the following:  is Artinian serial if and only if every  -module is a direct sum of extending modules if and only if  is left serial with every right  -module a direct sum of extending modules.
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Additional Information:
Noyan
Er
Affiliation:
Department of Mathematics, University of Rio Grande, Rio Grande, Ohio 45674
Email:
noyaner@yahoo.com
DOI:
10.1090/S0002-9939-09-09807-4
PII:
S 0002-9939(09)09807-4
Received by editor(s):
April 22, 2008,
Received by editor(s) in revised form:
August 21, 2008, and October 16, 2008
Posted:
January 30, 2009
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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