Douglas Geoffrey Northcott, FRS (31 December 1916,

London London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...

– 8 April 2005) was a British

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who worked on

ideal theory In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings (and this article therefore only consid ...

Early life and career

Northcott was born Douglas Geoffrey Robertson in Kensington on 31 December 1916 to Clara Freda (née Behl) (1894-1958) and her first husband Geoffrey Douglas Spence Robertson (1894-1978). His mother remarried in 1919 to Arthur Hugh Kynaston Northcott (1887-1952). In 1935, he legally adopted his step-father's surname. He was educated in London, then at

Christ's Hospital Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553 ...

and

St John's College, Cambridge St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...

, where he started research under the supervision of

G.H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

His work was interrupted by active service during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

. Captured at Singapore, he survived his time as a prisoner of war in Japan, and returned to Cambridge at the end of the war. Back at Cambridge, he published his dissertation "Abstract Tauberian theorems with applications to power series and Hilbert series ". He then turned to algebra under the influence of

Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing lar ...

, whom he had met while visiting

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. He became a Research Fellow of St John's College in 1948. In 1952, he moved to the Town Trust Chair of Pure Mathematics at

Sheffield University , mottoeng = To discover the causes of things , established = – University of SheffieldPredecessor institutions: – Sheffield Medical School – Firth College – Sheffield Technical School – University College of Sheffield , type = Pu ...

. He remained at Sheffield until his retirement in 1982, also serving as Head of Department and Dean of Pure Science. In 1954, Douglas Northcott and

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introduced in a joint paper the Northcott-Rees theory of reductions and integral closures, which has subsequently been influential in

commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...

Awards

Northcott was awarded the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

Junior

Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...

in 1953 and served as LMS Vice-President during 1968-69. He was elected

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 1961.

Family life

In 1949, at Cambridge, Northcott married Rose Hilda Austin (1917-1992), with two daughters, Anne Patricia (born 1950) and Pamela Rose (1952-1992).

Publications

* Northcott, D. G. ''Multilinear algebra.''

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

, Cambridge, 1984. * Northcott, D. G. ''A first course of homological algebra.'' Reprint of 1973 edition. Cambridge University Press, Cambridge-New York, 1980. * Northcott, D. G. ''Affine sets and affine groups.'' London Mathematical Society Lecture Note Series, 39. Cambridge University Press, Cambridge-New York, 1980. * Northcott, D. G. ''Finite free resolutions.'' Cambridge Tracts in Mathematics, No. 71. Cambridge University Press, Cambridge-New York-Melbourne, 1976. * Northcott, D. G. ''Lessons on rings, modules and multiplicities.'' Cambridge University Press, London 1968 * Northcott, D. G. ''An introduction to homological algebra.'' Cambridge University Press, New York 1960 * Northcott, D. G. ''Ideal theory.'' Cambridge Tracts in Mathematics and Mathematical Physics, No. 42. Cambridge, at the University Press, 1953.

References

20th-century British mathematicians People educated at Christ's Hospital Academics of the University of Sheffield World War II prisoners of war held by Japan Alumni of St John's College, Cambridge Fellows of St John's College, Cambridge Fellows of the Royal Society People from Kensington Algebraists 1916 births 2005 deaths {{UK-mathematician-stub