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ABSTRACT
A ring is partially one-sided unit-regular provided that, for each regular
, there is a right or left invertible element
such that
. It is shown that
is partially one-sided unit-regular if and only if every regular element in
is the product of an idempotent and a right or left invertible element. Morita contexts over partially one-sided unit-regular exchange rings are also studied.
ACKNOWLEDGMENTS
The author is grateful to the referee for his/her suggestions which led to the new version of Theorem 3.2 and helped me to improve the manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 19801012) and the Ministry of Education of China ([2000] 65).