Abstract We examine properties of the right ideal structure of right distributive domains. Right distributive domains R are exactly those rings whose localizations at maximal right ideals M are right chain domains R M - On the one hand, the paper focuses on the question in which way properties of R are carried over to R M and vice versa. We examine the problem under which conditions two-sided ideals of R are again two-sided in the extension R M (Lemma 2. 2). Further, we observe the relationship between completely prime resp. semiprime ideals of R and the extended ideals in R M. On the other hand, we prove in particular that for any maximal right ideal M = R M the right-S M -saturation of a completely semiprime ideal I M of R is completely prime (Theorem 2. 9). A central role is played by waists of right distributive rings which are right ideals comparable to each other ideal, in particular there exists a largest waist W which is completely prime. We present a representation theorem in terms of ideals in R W. We apply these results to the Jacobson radical J (R) of a right distributive domain R. Illustrative examples are given.
Törner et al. (Sun,) studied this question.
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