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Recently I discovered by accident that Bourbaki issued in 2012 a radically expanded version of their 1958 Chapter 8 Modules et anneaux semi-simples (like other chapters, initially in French) within the treatise Algebre: see webpage. Like others, I've assumed that the Bourbaki writing project ended decades ago, but this new edition published by Springer-Verlag adds some 300 pages to the modest 189 pages of the old Hermann edition I have. The earlier 13 sections, followed by an appendix on rings without unity, have now grown to 21 sections with four appendices. I have no inside information, but this raises a natural question:

Was the expanded edition of Chapter 8 written recently? (More broadly, does this presage some kind of revival of the Bourbaki writing project)?

This particular chapter has always struck me as more readable than average among those in algebra, partly because it is relatively self-contained and less opaque in its arguments than many other parts of their treatise. Naturally the choices made by Bourbaki in their foundational books (algebra, commutative algebra, general topology, ...) have been controversial, e.g., their avoidance of categories and functors. But it's clear that they had a far-reaching program in mind for replacing what they found in the literature of their time with a carefully organized and rigorous presentation. As the group evolved over the years, they also wrote usefully about more specialized matters, notably Lie theory. But much of their ambitious agenda remains incomplete. By now the ongoing activity seems to center almost exclusively on their Paris seminar.

P.S. I've edited the question to clarify the intent. I realize of course that the Bourbaki group has always operated anonymously, even though many past members became identifiable. The source of my question is partly curiosity about the future (if any) of the unfinished treatise on Lie groups and Lie algebras.

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    $\begingroup$ Bourbaki never mentioned authors names (in his publications). So the tradition is maintained. But often we know (or guess) who wrote what. That is the case for instance of Cartier, Demazure, Serre. $\endgroup$
    – Al-Amrani
    Jan 13, 2016 at 15:54
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    $\begingroup$ "Algèbre commutative, Chapitre 10" was published in 1998. I think the question is based on a false premise and not quite appropriate. $\endgroup$
    – user9072
    Jan 13, 2016 at 16:22
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    $\begingroup$ @quid: Given the known working habits of the Bourbaki group, I was assuming (perhaps incorrectly) that this small Chapter 10 was already in the pipeline for some years at the time of publication in 1998. The situation with Chapter 8 of Algebre looks different to me, since it apparently involved a complete rethinking and rewrting of the original text. (I haven't seen the e-book yet, while access issues to Five College libraries are being worked out, but I've compared the tables of contents.) So my question does seem reasonable (to me). $\endgroup$ Jan 13, 2016 at 18:29
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    $\begingroup$ That chapter has almost 200 pages, it seems not particularly small to me, but I guess I see your point. For 2016 the publication of Topologie algébrique, chapitres 1 à 4 is announced. A table of content is on Bourbaki's website. The main point rests: I do not find it appropriate to inquirer about authorship (close to the time of publication) when it is intentionally kept non-public. If Bourbaki wanted to make this (widely) known it'd be easy enough. Either way at least one of the main current public voices of Bourbaki is active on the site so I'll leave this. $\endgroup$
    – user9072
    Jan 13, 2016 at 18:48
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    $\begingroup$ There is still a question here that does not pry into the identity of Bourbaki: Can we expect any more Bourbaki writings to emerge in the near future? If so, what topics are planned and when can we expect them? MO is actually a rather good place for this kind of question because we can even hope for a user named "Bourbaki" to answer it, without compromising anonymity. $\endgroup$ Jan 19, 2016 at 4:07

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