Abstract
The rings referred to in the title of this paper have long been conjectured to be principal left ideal domains. In a recent paper [6] Cohn and Schofield have produced examples (of simple rings) showing that this is not the case. As a result, interest in this type of ring has deepened (see [5], for example, where these rings are referred to as right principal Bezout domains). Our main purpose here is to prove that such rings are either principal left ideal domains or left and right primitive rings.
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