Partial cancellation of modules |
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Authors: | H Chen |
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Institution: | (1) Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, People's Republic Of China |
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Abstract: | We investigate partial cancellation of modules and show that if an ideal I of an exchange ring R has stable range one, then A⊕B≌A⊕C implies B≌C for all A∈FP (I). The converse is true when R is a regular ring. For an ideal I of a regular ring, we also show that I has stable range one if and only if perspectivity is transitive in L(A) for all A∈ FP (I). These give nontrivial generalizations for unit-regularity.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | regular ring exchange ring partial cancellation |
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