Stable modules and a theorem of Camillo and Yu.

Abstract: In 1995, Camillo and Yu showed that an exchange ring has stable range 1 if and only if every regular element is unit-regular. An element m in a module is called regular if for some . In this paper we define stable modules and show that if M has the finite exchange property then M is stable if and only if, for every regular element , where is epic (and we say that m is unit-regular). Such modules are called regular-stable. It is shown that is regular-stable if and only if R has internal cancellation. To simplify the exposition, many arguments are formulated in an arbitrary Morita context. [Copyright &y& Elsevier]