A user over at MSE flagged https://math.stackexchange.com/questions/455506/why-cohen-macaulay-rings-have-become-important-in-commutative-algebra#question suggesting that it is suitable for MO.

The question is a bit soft (it asks "I want to know the historic reasons behind singling out Cohen-Macaulay rings as interesting algebraic objects"), and is possibly opinion based, so I am hesitant about migrating the question. As phrased it may also be quite broad (though it may also be not broad at all; I'm not really great with commutative algebra).

Hence this question: what do people think? Would this question be something that fits on MO?

  • 2
    $\begingroup$ The formulation is not really optimal in my opinion, the 'singling out' in particular, but in general question on the relevance and the origin of the notion Cohen-Macaulay ring seems alright. There is a well-known paper by Bass 'On the ubiquity of Gorenstain rings' for example, so to elaborate on why a class of rings is relevant and where it appears is something that has merit. Regarding 'opinion based' I wouldn't be too worried; I think it is a math question why it is so interesting if all loc. of a ring have same Krull dim. as depth that one calls them CM then and books exist on them. $\endgroup$
    – user9072
    Commented Jul 30, 2013 at 14:31
  • $\begingroup$ Seems reasonable enough to me. $\endgroup$ Commented Jul 30, 2013 at 23:41

1 Answer 1


Okay, it has been done. The question now lives at

Why Cohen-Macaulay rings have become important in commutative algebra?

here on MO.


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