A characterization of cancellation ideals
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- by D. D. Anderson and Moshe Roitman PDF
- Proc. Amer. Math. Soc. 125 (1997), 2853-2854 Request permission
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
- 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
- Irving Kaplansky, Topics in commutative ring theory, University of Chicago, Department of Mathematics, Chicago, Ill., 1974. Lecture notes. MR 0427288
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
- Received by editor(s): May 16, 1996
- Additional Notes: M. Roitman thanks the University of Iowa for its hospitality.
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1997 American Mathematical Society
- 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