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I would like to see some (or many!) examples of noncommutative Bezout domains (one-sided principal ideals sum to one-sided principal ideals). I've read somewhere that it's not easy to find an example of a right but not left Bezout domain, but even though I would be glad to see it, I'm actually more interested in examples of domains that are Bezout on both sides. (And of course aren't PIDs.) A Google search gave me nothing, as did a search on this site.

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  • $\begingroup$ Made CW at OP's suggestion. $\endgroup$
    – Todd Trimble
    Sep 22, 2014 at 20:47

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See the paper:

P. M. Cohn, MR 153696 Rings with a weak algorithm, Trans. Amer. Math. Soc. 109 (1963), 332--356.See the paper "Rings with a weak algorithm" by P. M. Cohn.

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  • $\begingroup$ I just edited your answer to include a more full citation. However, you might also consider including a summary as to why this paper is relevant. For example, what is a specific example in this paper which helps answer the question. $\endgroup$ Feb 7, 2017 at 18:24

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