Abstract:A left [right] chain ring is a ring with identity in which the left [right] ideals are totally ordered by inclusion, and a chain ring is a ring that is both a left and right chain ring. Recently, Lorimer showed that the nondiscrete compact rings that are right (or left) chain rings are precisely the compact, discrete valuation rings, that is, the valuation rings of nondiscrete locally compact division rings. Here we show that the complete, discrete valuation rings of division rings are precisely the nondiscre… Show more
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