Comparability, separativity, and exchange rings
نویسندگان
چکیده
منابع مشابه
Elements in Exchange Rings with Related Comparability
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.
متن کاملCountable Exchange and Full Exchange Rings
We show that a Dedekind-finite, semi-π-regular ring with a “nice” topology is an א0-exchange ring, and the same holds true for a strongly clean ring with a “nice” topology. We generalize the argument to show that a Dedekind-finite, semi-regular ring with a “nice” topology is a full exchange ring. Putting these results in the language of modules, we show that a cohopfian module with finite excha...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 1996
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927879608825721