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A Characterization of Cancellation Ideals

Author(s): D. D. Anderson; Moshe Roitman
Journal: Proc. Amer. Math. Soc. 125 (1997), 2853-2854.
MSC (1991): Primary 13A15
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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:

1.: R. Gilmer, Multiplicative ideal theory, Queen's Papers in Pure and Applied Mathematics, vol. 90, Queen's University, Kingston, Ontario, 1992. MR 93j:13001
2.: I. Kaplansky, Topics in commutative ring theory, unpublished notes, 1971. MR 55:322


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