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On τ-completely decomposable modules

Published online by Cambridge University Press:  17 April 2009

Septimiu Crivei
Septimiu Crivei
Affiliation:
Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. M. Kogălniceanu 1, RO-400084 Cluj-NapocaRomania, e-mail: crivei@math.ubbcluj.ro
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For a hereditary torsion theory τ, a module A is called τ-completedly decomposable if it is a direct sum of modules that are the τ-injective hull of each of their non-zero submodules. We give a positive answer in several cases to the following generalised Matlis' problem: Is every direct summand of a τ-completely decomposable module still τ-completely decomposable? Secondly, for a commutative Noetherian ring R that is not a domain, we determine those torsion theories with the property that every τ-injective module is an essential extension of a (τ-injective) τ-completely decomposable module.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 163 - 175
Copyright
Copyright © Australian Mathematical Society 2004

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