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 land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

who worked on

local ring In abstract algebra, more specifically 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 varieties or manifolds, or of algebraic n ...

s. He was a student of

Oscar Zariski , birth_date = , birth_place = Kobrin, Russian Empire , death_date = , death_place = Brookline, Massachusetts, United States , nationality = American , field = Mathematics , work_institutions = ...

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...

. In his thesis he proved the

Cohen structure theorem In mathematics, the Cohen structure theorem, introduced by , describes the structure of complete Noetherian local rings. Some consequences of Cohen's structure theorem include three conjectures of Krull: *Any complete regular equicharacteristic ...

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 lengt ...

s. In 1946 he proved the unmixedness theorem for power series rings. As a result,

Cohen–Macaulay ring In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebraic geometry, algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly ...

s 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 Systems ...

. 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 Andr ...

. 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

* * * * * * *

References

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