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Ideals generated by powers of elements

Published online by Cambridge University Press:  17 April 2009

D.D. Anderson ,
Kent R. Knopp  and
Rebecca L. Lewin
D.D. Anderson
Affiliation:
Department of MathematicsThe University of IowaIowa City, IA 52242United States of America
Kent R. Knopp
Affiliation:
Department of MathematicsMt. Mercy CollegeCedar Rapids, IA 52402United States of America
Rebecca L. Lewin
Affiliation:
Department of MathematicsUniversity if Wisconsin - La CrosseLa Crosse, WI 54601United States of America
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For an ideal I in a commutative ring R we consider the ideal In = ({in | i ∈I}). We show that if n! is a unit in R, then In = In. We give an example of a doubly generated ideal I with Is not finitely generated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 373 - 376
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, D.D. and Zafrullah, M., ‘Almost Bézout domains’, J. Algebra 142 (1991), 285–309.CrossRefGoogle Scholar
[2]Kaplansky, I., Commutative Rings, Revised Edition (University of Chicago Press, Chicago, 1974).Google Scholar