ABSTRACT
A ring R is said to have the finitely generated cancellation property provided that the module isomorphism R⊕B≅R⊕C implies B≅C for any finitely generated R-modules B and C. It is proved that R has this property is equivalent to the existence of the cancellation matrices over R. Moreover, the structure of such matrices is investigated and finite weakly stable rings are characterized in terms of their cancellation matrices.
Acknowledgments
The author would like to thank the referee for many valuable and thoughtful comments which improve this paper considerably; and thank my friend, Prof. Chen Weixing, for helping me to improve the presentation.