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Communications in Algebra Volume 32, 2004 - Issue 10
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Original Articles

Some Remarks on Multiplication and Projective Modules

Majid M. Ali Department of Mathematics, Sultan Qaboos University, Muscat, Oman; Department of Mathematics, Sultan Qaboos University, Muscat, OmanCorrespondence[email protected]
&
David J. Smith Department of Mathematics, University of Auckland, Auckland, New Zealand
Pages 3897-3909 | Received 01 Apr 2003, Published online: 24 Jun 2011
 
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Abstract

The associated ideal θ(M) and the trace ideal T(M) of a module M play analogous but distinct roles in the study of multiplication and projective modules respectively. We further investigate both and show in particular that faithful multiplication and projective modules have common properties. We use a method based on Anderson's characterizations of multiplication modules which enables new proofs of theorems on multiplication modules of El Bast, Low, Smith and Smith, and then, also enables similar results for projective modules.

AMS Classification (2000):

Acknowledgments

Notes

#Communicated by A. Facchini.

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