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NEAT AND CONEAT SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Published online by Cambridge University Press:  07 August 2013

SEPTIMIU CRIVEI*
Affiliation:
Faculty of Mathematics and Computer Science, ‘Babeş-Bolyai’ University, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania email crivei@math.ubbcluj.ro
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Abstract

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We prove that neat and coneat submodules of a module coincide when $R$ is a commutative ring such that every maximal ideal is principal, extending a recent result by Fuchs. We characterise absolutely neat (coneat) modules and study their closure properties. We show that a module is absolutely neat if and only if it is injective with respect to the Dickson torsion theory.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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NEAT AND CONEAT SUBMODULES OF MODULES OVER COMMUTATIVE RINGS
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