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I've recently been involved in a math conversation regarding partial fraction decompositions for rational numbers, but we seem to lack a formal definition and are unsure about whether there is some kind of uniqueness statement.

Can someone please provide a solid reference for partial fraction decompositions for integral domains, assuming that this makes sense? (This topic is mentioned ever so briefly in the Wikipedia article about PFD's, but without an existing reference.)

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    $\begingroup$ Does this answer answer your question? It appears that this can be done only for Euclidean domains, in almost the same way as for polynomials. $\endgroup$
    – Iosif Pinelis
    Commented Jun 15, 2023 at 18:23
  • $\begingroup$ That answer looks very helpful, thanks! (Except for its mention of the Wikipedia page, which is not.) $\endgroup$
    – Daniel Asimov
    Commented Jun 15, 2023 at 18:44
  • $\begingroup$ But I would like to see a reference to a textbook or peer-reviewed paper. $\endgroup$
    – Daniel Asimov
    Commented Jun 15, 2023 at 18:46
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    $\begingroup$ Packard and Wilson, "Partial fractions in Euclidean domains" (1989) (MR0991540) $\endgroup$
    – Dave Benson
    Commented Jun 15, 2023 at 19:07
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    $\begingroup$ Thank you, Dave Benson. That is exactly the kind of thing I was looking for. $\endgroup$
    – Daniel Asimov
    Commented Jun 15, 2023 at 19:47

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