Elements in Exchange Rings with Related Comparability
نویسنده
چکیده
We show that if R is an exchange ring, then the following are equivalent: (1) R satisfies related comparability. (2) Given a,b,d ∈ R with aR+bR = dR, there exists a related unit w ∈ R such that a+bt = dw. (3) Given a,b ∈ R with aR = bR, there exists a related unit w ∈ R such that a= bw. Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.
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تاریخ انتشار 2000