Ideals generated by powers of elements

D.D. Anderson; K.R. Knopp; R.L. Lewin

doi:10.1017/S0004972700016488

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Ideals generated by powers of elements

D.D. Anderson, K.R. Knopp and R.L. Lewin

Bulletin of the Australian Mathematical Society, Vol.49(3), pp.373-376

1994

DOI: 10.1017/S0004972700016488

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Abstract

For an ideal I in a commutative ring R we consider the ideal In = ({in | i [formula omitted]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. © 1994, Australian Mathematical Society. All rights reserved.

Details

Title: Subtitle: Ideals generated by powers of elements
Creators: D.D. Anderson - University of Iowa
K.R. Knopp - Mercy University
R.L. Lewin - Department of Mathematics University if Wisconsin - La Crosse La Crosse, WI 54601 United States of America
Resource Type: Journal article
Publication Details: Bulletin of the Australian Mathematical Society, Vol.49(3), pp.373-376
DOI: 10.1017/S0004972700016488
ISSN: 0004-9727
Comment: References: Anderson, D.D., Zafrullah, M., Almost Bézout domains (1991) J. Algebra, 142, pp. 285-309; Kaplansky, I., (1974) Commutative Rings, , Revised Edition (University of Chicago Press, Chicago)
Language: English
Date published: 1994
Academic Unit: Mathematics
Record Identifier: 9984230625702771

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