Anderson, D. D.; Roitman, Moshe A characterization of cancellation ideals. (English) Zbl 0883.13001 Proc. Am. Math. Soc. 125, No. 10, 2853-2854 (1997). Summary: 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. Cited in 1 ReviewCited in 17 Documents MSC: 13A15 Ideals and multiplicative ideal theory in commutative rings Keywords:cancellation ideal; regular principal ideal PDFBibTeX XMLCite \textit{D. D. Anderson} and \textit{M. Roitman}, Proc. Am. Math. Soc. 125, No. 10, 2853--2854 (1997; Zbl 0883.13001) Full Text: DOI References: [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. · Zbl 0804.13001 [2] Irving Kaplansky, Topics in commutative ring theory, Department of Mathematics, University of Chicago, Chicago, Ill., 1974. Lecture notes. · Zbl 0348.13001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.