Weakly Stable Modules |
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| Authors: | Hongbo Zhang Wenting Tong |
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| Institution: | Department of Mathematics , Nanjing University , Nanjing, China |
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| Abstract: | ABSTRACT A new notion which is called weakly stable module is introduced in this article. It is a nontrivial generalization of the modules with endomorphism rings having stable range one. We deduce that weakly stable projective modules have the cancellation property, and so any commutative hereditary ring has the cancellation property, i.e., if R is a commutative hereditary ring, then for any R-modules B and C, R ⊕ B ? R ⊕ C implies B ? C. |
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| Keywords: | Hereditary rings Stable range one The cancellation property |
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