Stable Modules and a Theorem of Camillo and Yu
نویسنده
چکیده
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 RM is called regular if (mλ)m = m for some λ ∈ hom(M,R). 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 m ∈ M, (mγ)m = m where γ : M → R is epic (and we say that m is unit regular). Such modules are called regular stable. It is shown that RR is regular-stable if and only if R has internal cancellation. To simplify the exposition, many arguments are formulated in an arbitrary Morita context.
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