A ring R (with unit element) is called a duo ring if every one-sided ideal is two-sided. This is equivalent with the existence of elements r' and r u in R with rs = sr f , sr = r"s for elements r, s in R. We will discuss in this note the following three problems: (A) Is the localization at a prime ideal P of a duo ring again a duo ring? (B) Is in a duo ring the P -component of zero equal to the right (left) P-component of zero? (C) Is in a noetherian duo domain the semi group of ideals (under multiplication) commutative?
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Hans-Heinrich Brungs (1975) studied this question.
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