Alfred William Goldie (10 December 1920, Coseley,

Staffordshire Staffordshire (; postal abbreviation ''Staffs''.) is a Ceremonial counties of England, ceremonial county in the West Midlands (region), West Midlands of England. It borders Cheshire to the north-west, Derbyshire and Leicestershire to the east, ...

– 8 October 2005,

Barrow-in-Furness Barrow-in-Furness is a port town and civil parish (as just "Barrow") in the Westmorland and Furness district of Cumbria, England. Historic counties of England, Historically in the county of Lancashire, it was incorporated as a municipal borou ...

Cumbria Cumbria ( ) is a ceremonial county in North West England. It borders the Scottish council areas of Dumfries and Galloway and Scottish Borders to the north, Northumberland and County Durham to the east, North Yorkshire to the south-east, Lancash ...

) was an

English English usually refers to: * English language * English people English may also refer to: Culture, language and peoples * ''English'', an adjective for something of, from, or related to England * ''English'', an Amish ter ...

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, mathematical structure, structure, space, Mathematica ...

Biography

Goldie was educated at

Wolverhampton Grammar School Wolverhampton Grammar School is a co-educational private school in Wolverhampton, England. History Initially a grammar school for boys, WGS was founded in 1512 by Sir Stephen Jenyns, a master of the ancient guild of Merchant Taylors, who was ...

and then read

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at St John's College,

Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...

. His studies were interrupted by war work on

ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and acceler ...

with the Armament Research Department of the

Ministry of Supply The Ministry of Supply (MoS) was a department of the UK government formed on 1 August 1939 by the Ministry of Supply Act 1939 ( 2 & 3 Geo. 6. c. 38) to co-ordinate the supply of equipment to all three British armed forces, headed by the Ministe ...

, eventually taking his BA in 1942 and MA in 1946.

Academic career

Goldie became an assistant

lecturer Lecturer is an academic rank within many universities, though the meaning of the term varies somewhat from country to country. It generally denotes an academic expert who is hired to teach on a full- or part-time basis. They may also conduct re ...

at the

University of Nottingham The University of Nottingham is a public research university in Nottingham, England. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. Nottingham's main campus (University Park Campus, Nottingh ...

in 1946. In 1948 he was appointed lecturer in

Pure Mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

at what was then

King's College, Durham Newcastle University (legally the University of Newcastle upon Tyne) is a public research university based in Newcastle upon Tyne, England. It has overseas campuses in Singapore and Malaysia. The university is a red brick university and a memb ...

(and has been the

University of Newcastle upon Tyne Newcastle University (legally the University of Newcastle upon Tyne) is a public university, public research university based in Newcastle upon Tyne, England. It has overseas campuses in Singapore and Malaysia. The university is a red brick un ...

since 1963) where he was promoted to senior lecturer in 1958 and reader in

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

in 1960. In 1963 Goldie was appointed

Professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

at the

University of Leeds The University of Leeds is a public research university in Leeds, West Yorkshire, England. It was established in 1874 as the Yorkshire College of Science. In 1884, it merged with the Leeds School of Medicine (established 1831) and was renamed Y ...

. He retired from his chair in 1986 with the title

emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

. Goldie won the 1970

Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Stat ...

from the

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

, where he also served as vice-president from 1978 to 1980. Goldie worked in ring theory, where he introduced the notion of the

uniform dimension In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of ''M'' is an essential submodule. A ring may be called a right (left ...

of a module, and the reduced rank of a module. He is well known for

Goldie's theorem In mathematics, Goldie's theorem is a basic structural result in ring theory, proved by Alfred Goldie during the 1950s. What is now termed a right Goldie ring is a ring ''R'' that has finite uniform dimension (="finite rank") as a right module o ...

, which characterizes right Goldie rings. Indeed, his ''

Independent Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist ...

'' obituary described him as the "Lord of the Rings".

Personal life

Goldie married Mary Kenyon in 1944. They had three children (from eldest to youngest): Isobel (Carlyle), Helen, and John. Both Isobel and Helen completed PhDs in Geography, while John completed a degree in Music. Mary died in 1995 and in 2002 he married Margaret Turner, who survived him.

References

Mathematics People, Notices AMS
*S C Coutinho and J C McConnell
The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)
Amer. Math. Monthly 110 (4) (2003), 298-313. *J J O'Connor and E F Robertson

*Mathematics Genealogy Project
doctoral students of Alfred Goldie
{{DEFAULTSORT:Goldie, Alfred 1920 births 2005 deaths 20th-century English mathematicians People educated at Wolverhampton Grammar School Alumni of St John's College, Cambridge Academics of the University of Nottingham Academics of the University of Leeds People from Coseley