The Cancellation Law for Ideals in a Commutative Ring
- 1 January 1965
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 17, 281-287
- https://doi.org/10.4153/cjm-1965-028-3
Abstract
We say that therestricted cancellation lawfor ideals (RCL) holds in the commutative ringRif from the equationAB=AC, whereA,B, andCare ideals ofRandAB≠ (0), it follows thatB=C. RCL is a weakened form of thecancellation lawfor ideals (CL) : IfA,B, andCare ideals ofRsuch thatAB=ACandA≠ (0), thenB=C. A ring in which CL holds is an integral domain and in an integral domain, RCL is equivalent to CL.Keywords
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