Irvin Sol Cohen (1917 – February 14, 1955) was an American mathematician at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

who worked on

local ring In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on algebraic varieties or manifolds, or of ...

s. He was a student of Oscar Zariski at

Johns Hopkins University The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J ...

. In his thesis he proved the Cohen structure theorem for complete

Noetherian In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite leng ...

s. In 1946 he proved the unmixedness theorem for power series rings. As a result, Cohen–Macaulay rings are named after him and

Francis Sowerby Macaulay Francis Sowerby Macaulay FRS (11 February 1862, Witney – 9 February 1937, Cambridge) was an English mathematician who made significant contributions to algebraic geometry. He is known for his 1916 book ''The Algebraic Theory of Modular Syste ...

. Cohen and

Abraham Seidenberg Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician. Early life Seidenberg was born on June 2, 1916, to Harry and Fannie Seidenberg in Washington D.C. He graduated with a B.A. from the University of Maryland in 1937 ...

published their Cohen–Seidenberg theorems, also known as the going-up and going-down theorems. He also coauthored articles with

Irving Kaplansky Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St And ...

. One of his doctoral students was R. Duncan Luce.

Death

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

Publications

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References

* * * * 1917 births 1955 suicides 1955 deaths 20th-century American mathematicians Johns Hopkins University alumni Massachusetts Institute of Technology faculty American algebraists {{US-mathematician-stub