Uniquely exchange rings


Fatemeh Rashedi




An associative ring $R$ with unity is called exchange if every element $a\in R$ is exchange, i.e., there exists an idempotent $e\in aR$ such that $1-e\in(1-a)R$; if this representation is unique for every element, we call the ring uniquely exchange. We give a complete description of uniquely exchange rings.