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A characterization of cancellation ideals. (English) Zbl 0883.13001

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.

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
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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
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