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Rings that are FGC relative to filters of ideals

Published online by Cambridge University Press:  20 January 2009

Erol Barbut  and
Willy Brandal
Erol Barbut
Affiliation:
Department of Mathematics and StatisticsUniversity of IdahoMoscow, ID 83843USA
Willy Brandal
Affiliation:
Department of Mathematics and StatisticsUniversity of IdahoMoscow, ID 83843USA
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All our rings will be commutative with identity not equal to zero. Also R will always denote a ring. is a filter of ideals of R if is a nonempty set of ideals of R satisfying: I∈ and J is an ideal of R with I⊂J, then J∈, and if I, J∈ then I∩J∈. A Gabriel topology of R is a filter of ideals of R satisfying: if J∈ and I is an ideal of R with (I:x)∈ for all x∈J, then I∈. See the B. Stenström text [6]. We say that a ring R is an FGC ring if every finitely generated R-module is a direct sum of cyclic R-modules. Use mspec R for the set of all maximal ideals of R.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 11 - 18
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

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