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A Characterization of Cancellation Ideals


Authors: D. D. Anderson and Moshe Roitman
Journal: Proc. Amer. Math. Soc. 125 (1997), 2853-2854
MSC (1991): Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-97-04042-2
MathSciNet review: 1415571
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Abstract: An ideal $I$ of a commutative ring $R$ with identity is called a cancellation ideal if whenever $IB=IC$ for ideals $B$ and $C$ of $R$, then $B=C$. We show that an ideal $I$ is a cancellation ideal if and only if $I$ is locally a regular principal ideal.


References [Enhancements On Off] (What's this?)

  • 1. Robert Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, vol. 90, Queen’s University, Kingston, ON, 1992. Corrected reprint of the 1972 edition. MR 1204267
  • 2. Irving Kaplansky, Topics in commutative ring theory, Department of Mathematics, University of Chicago, Chicago, Ill., 1974. Lecture notes. MR 0427288

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Additional Information

D. D. Anderson
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: dan-anderson@uiowa.edu

Moshe Roitman
Affiliation: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Email: mroitman@mathcs2.haifa.ac.il

DOI: https://doi.org/10.1090/S0002-9939-97-04042-2
Keywords: Cancellation ideal
Received by editor(s): May 16, 1996
Additional Notes: M. Roitman thanks the University of Iowa for its hospitality.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society