# Irvin Cohen

**Irvin Sol Cohen** (1917 – February 14, 1955) was an American mathematician at MIT who worked on local rings. He was a student of Oscar Zariski at Johns Hopkins University.

Irvin S. Cohen | |
---|---|

Born | 1917 |

Died | 14 February 1955 |

Nationality | United States |

Alma mater | Johns Hopkins University (Ph.D., 1942) |

Known for | Cohen-Macaulay rings, Cohen structure theorem, Cohen-Seidenberg theorems, unmixedness theorem, Cohen rings |

Scientific career | |

Fields | Mathematics |

Institutions | MIT |

Doctoral advisor | Oscar Zariski |

In his thesis he proved the Cohen structure theorem for complete Noetherian local rings.^{[1]} 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, also known as the going-up and going-down theorems. He also coauthored articles with Irving Kaplansky.

## DeathEdit

Cohen died unexpectedly in 1955 one week after having visited Zariski in Cambridge, apparently from suicide. Many years later Zariski said of his death:^{[1]}

Many things are necessary to make a good scientist, a creative man, and left on his own Cohen found himself unproductive. Highly critical of himself and others, he believed that nothing he ever wrote was as good as his thesis. He became increasingly involved with abstract algebra until he found himself at a certain point without ground under his feet. He became disappointed in his work, and finally, fatally, in his own ability.

## PublicationsEdit

- 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. - Cohen, I.S.; Seidenberg, A. (1946). "Prime ideals and integral dependence".
*Bull. Amer. Math. Soc*.**52**(4): 252–261. MR 0015379. - Cohen, I.S.; Kaplansky, Irving (1946). "Rings With a Finite Number of Primes. I".
*Trans. Amer. Math. Soc*.**60**(3): 468–477. - Cohen, I.S. (1950). "Commutative rings with restricted minimum condition".
*Duke Math. J*.**71**(1). - Cohen, I.S. (1954). "Length of prime ideal chains".
*American J. Math*.**76**(3): 654–668. - Cohen, I.S.; Kaplansky, Irving (1951). "Rings for which every module is a direct sum of cyclic modules".
*Mathematische Zeitschrift*.**54**(1): 97–101. - Cohen, I.S.; Zariski, Oscar (1957). "A fundamental inequality in the theory of extensions of valuations".
*Illinois J. Math*.**1**(1): 1–8.

## ReferencesEdit

- ^
^{a}^{b}Parikh 2014.

- Irvin Cohen at the Mathematics Genealogy Project
- Parikh, Carol (2014).
*The Unreal Life of Oscar Zariski*. Academic Press. p. 64. ASIN B01DUEBQSC. - "News and Notices".
*American Mathematical Monthly*.**62**(4): 296. 1955. JSTOR 2306718. - The Mathematical Association of America. "Report of the Treasurer for the Year 1954": 296. doi:10.1080/00029890.1955.11988629.

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