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The Cancellation Law for Ideals in a Commutative Ring

Published online by Cambridge University Press:  20 November 2018

Robert W. Gilmer Jr.
Robert W. Gilmer Jr.*
Affiliation:
Florida State University, Tallahassee, Florida
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We say that the restricted cancellation law for ideals (RCL) holds in the commutative ring R if from the equation AB = AC, where A, B, and C are ideals of R and AB ≠ (0), it follows that B = C. RCL is a weakened form of the cancellation law for ideals (CL) : If A, B, and C are ideals of R such that AB = AC and A ≠ (0), then B = C. A ring in which CL holds is an integral domain and in an integral domain, RCL is equivalent to CL.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 281 - 287
Copyright
Copyright © Canadian Mathematical Society 1965

References

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