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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the rings whose injective hulls are flat


Authors: K. Khashyarmanesh and Sh. Salarian
Journal: Proc. Amer. Math. Soc. 131 (2003), 2329-2335
MSC (2000): Primary 13C11, 13H10
Published electronically: January 28, 2003
MathSciNet review: 1974629
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $R$ be a commutative Noetherian ring with nonzero identity and let the injective envelope of $R$ be flat. We characterize these kinds of rings and obtain some results about modules with nonzero injective cover over these rings.


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Additional Information

K. Khashyarmanesh
Affiliation: Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran – and – Department of Mathematics, Damghan University, P.O. Box 36715-364, Damghan, Iran
Email: khashyar@mail.ipm.ir

Sh. Salarian
Affiliation: Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran – and – Department of Mathematics, Damghan University, P.O. Box 36715-364, Damghan, Iran

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06829-1
PII: S 0002-9939(03)06829-1
Keywords: Injective envelope, flat cover, injective cover, Gorenstein ring, Gorenstein injective module
Received by editor(s): May 11, 2001
Received by editor(s) in revised form: March 26, 2002
Published electronically: January 28, 2003
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2003 American Mathematical Society