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On -complete filters

Part of: Theory of modules and ideals

Published online by Cambridge University Press:  26 February 2010

A. Laradji
A. Laradji
Affiliation:
Universit de Sidi-Bel-Abbs, BP No 89, 22000, Sidi-Bel-Abbs, Algeria.
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Extract

Filters and אּ-complete filters can be used to produce set-theoretic extensions of direct sums and direct products. They can be applied to generalize theorems in module theory which involve these. For example, the theorem, stating that a ring is noetherian, if, and only if, direct sums of injectives are injective, can be generalized, provided we replace noetherian by Xa-noetherian and direct sums by אּ- complete filter sums with a suitable property.

MSC classification

Secondary: 13C99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 107 - 115
Copyright
Copyright University College London 1989

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References

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