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New characterization of  -injective modules
Author(s):
K.
I.
Beidar;
S.
K.
Jain;
Ashish
K.
Srivastava
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3461-3466.
MSC (2000):
Primary 16D50, 16P40
Posted:
May 19, 2008
MathSciNet review:
2415029
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Additional information
Abstract:
We provide a new characterization for an injective module to be  -injective.
References:
-
- 1.
- H. Bass, Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 0157984 (28:1212)
- 2.
- K. I. Beidar and W.-F. Ke, On essential extensions of direct sums of injective modules, Archiv. Math. (Basel) 78 (2002), 120-123. MR 1888412 (2003a:16006)
- 3.
- A. Cailleau, Une caractérisation des modules
 -injectifs, C. R. Acad. Sci. Paris Ser. A-B 269 (1969), A997-999. MR 0260782 (41:5405) - 4.
- C. Faith, Rings with ascending chain condition on annihilators, Nagoya Math. J. 27 (1966), 179-191. MR 0193107 (33:1328)
- 5.
- C. Faith and E. A. Walker, Direct-sum representations of injective modules, Journal of Algebra 5 (1967), 203-221. MR 0207760 (34:7575)
- 6.
- J. M. Goursaud and J. Valette, Sur l'enveloppe des anneaux de groupes réguliers, Bull. Math. Soc. France 103 (1975), 91-102. MR 0379569 (52:474)
- 7.
- C. Megibben, Countable injective modules are sigma-injective, Proc. Amer. Math. Soc. 84 (1982), 8-10. MR 633266 (83a:16030)
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Additional Information:
K.
I.
Beidar
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
S.
K.
Jain
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
jain@math.ohiou.edu
Ashish
K.
Srivastava
Affiliation:
Department of Mathematics and Computer Science, St. Louis University, St. Louis, Missouri 63103
Email:
asrivas3@slu.edu
DOI:
10.1090/S0002-9939-08-09420-3
PII:
S 0002-9939(08)09420-3
Keywords:
Injective modules,
$\Sigma $-injective modules,
essential extensions,
right noetherian rings.
Received by editor(s):
July 16, 2006,
Received by editor(s) in revised form:
February 12, 2007, May 24, 2007, July 27, 2007, and September 15, 2007
Posted:
May 19, 2008
Additional Notes:
The first author is deceased
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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