In 1946 he proved the unmixedness theorem for power series rings. As a result Cohen–Macaulay rings are named after him and F. S. Macaulay. Cohen and Seidenberg published their Cohen-Seidenberg theorems. He proved the Cohen structure theorem for complete Noetherian local rings.
- Irvin Cohen at the Mathematics Genealogy Project
- Cohen, I. S. (1946). "On the structure and ideal theory of complete local rings". Trans. Amer. Math. Soc. 59 (1): 54–106. doi:10.2307/1990313.
- "News and Notices". American Mathematical Monthly 62 (4): 296. 1955. JSTOR 2306718.
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