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One of Auslanders famous theorems is that he proved that the global dimension of a semiprimary ring is equal to the maximum of the projective dimensions of the simple modules of the ring. This result can be found in the book of Auslander, Reiten and Smalo or in the module theory book of Lam. But in both books I found no refence to the original article where Auslander proved it.

What was the original article where Auslander proved this?

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    $\begingroup$ I think there’s a typo in the question? But is this the paper you’re after: projecteuclid.org/download/pdf_1/euclid.nmj/1118799684 ? $\endgroup$
    – Jeremy Rickard
    Commented Dec 26, 2017 at 13:34
  • $\begingroup$ @JeremyRickard Thanks, the article is earlier than I expected. You can put this as an answer and I can accept it if you like. $\endgroup$
    – Mare
    Commented Dec 26, 2017 at 13:39
  • $\begingroup$ @JeremyRickard Oh I forgot to write "of the simple modules". Thanks $\endgroup$
    – Mare
    Commented Dec 26, 2017 at 13:41

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I think you probably want the following paper.

Auslander, Maurice, On the dimension of modules and algebras. III. Global dimension, Nagoya Math. J. 9, 67-77 (1955). ZBL0067.27103.

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