The cancellable range of rings |
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| Authors: | Hongbo Zhang Wenting Tong |
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| Affiliation: | (1) Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China;(2) Department of Information Science, Jiangsu Polytechnic University, Changzhou, Jiangsu, 213016, P.R. China |
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| Abstract: | We unify the cancellation property of rings with stable range one and the principal ideal domain by introducing a new notion which is called “cancellable range”. It is proved that if a ring R has cancellable range n for some positive integer n, then for any n-generated module B and any module  implies B ≅ C; if R is a Noetherian ring and R has cancellable range n for any n ≧ 1, then R has the cancellation property. Received: 16 November 2004 |
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| Keywords: | 16D70 16D40 16E50 |
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