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New characterization of $ \Sigma$-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
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Abstract: We provide a new characterization for an injective module to be $ \Sigma$-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 $ \Sigma$-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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