2005•Unpublished venueRequires access
Some cancellation ideal rings.
Sureeporn Chaopraknoi, K. Savettaseranee, P. Lertwichitsilp
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Abstract
An ideal I of a commutative ring R is called a cancellation ideal of R if for any ideals A, B of R, AI = BI implies A = B, and we call R a cancellation ideal ring if every nonzero ideal of R is a cancellation ideal. Our purpose is to show that the ring (mZ, +, ·) is always a cancellation ideal ring and the nontrivial ring (mZn, +, ·) is a n cancellation ideal ring if and only if is a prime and n ∤ (m, n)2 (m, n) where (m, n) denotes the g.c.d. of m and n.