**Alfred William Goldie, mathematician: born Coseley, Staffordshire 10 December 1920; Assistant Lecturer, Nottingham University 1946-48; Lecturer, then Senior Lecturer, Newcastle University 1948-63; Professor of Pure Mathematics, Leeds University 1963-86; married 1944 Mary Kenyon (died 1995; one son, two daughters), 2002 Margaret Turner; died Barrow in Furness, Cumbria 8 October 2005.**

Alfred W. Goldie was known to mathematicians around the world as a leading exponent of the branch of algebra called "ring theory" - indeed some of them referred to him with affection as "Alfred, Lord of the Rings". He was a vivid personality with an individual mind, full of opinions and strongly argued positions on mathematics but also on the wider world, including politics, where his views moved rightwards over the years - starting with Communism whilst a student at Cambridge, and ending well within traditional Conservatism.

From Wolverhampton Grammar School, Goldie won a scholarship to St John's College, Cambridge, taking a First in Part 2 of the Mathematical Tripos in 1941, after just two years. His abilities brought him to the attention of C.P. Snow, who arranged that his Second World War contribution should be to apply his mathematical skills in ballistics, spending some time at the Woolwich Arsenal and some at a base near Glasgow.

At the same time as working on ballistics, he kept in contact with the leading algebraist Phillip Hall, who helped guide his reading and his first research in algebra. After the war, he began his formal academic career, moving via Nottingham and then Newcastle to his final position - a Chair in Pure Mathematics at Leeds University, 1963-86.

His research started by studying general algebraic systems (Universal Algebra). However, in the 1950s he began to concentrate on ring theory, first, jointly with F.F. Bonsall, in applications to functional analysis, and then in noncommutative ring theory itself. His breakthrough came at the end of the 1950s when he published a pair of papers in the Proceedings of the London Mathematical Society ("The Structure of Prime Rings Under Ascending Chain Conditions", 1958, and "Semi-prime Rings With Maximum Condition", 1960) which quite simply revolutionised the area. The outcome was "Goldie's Theorem", which establishes that certain apparently abstract and hazy entities are actually matrices - albeit of a somewhat general nature. More technically, he showed that, by allowing some fractions, the rings involved were just matrix rings over non-commutative fields.

This result came as a huge surprise, since it had been unsuspected, and it was hailed as a most considerable advance. It led to invitations to work in other institutions, including Yale University, the Institut des Hautes Etudes Scientifiques in Paris and Tulane University in New Orleans. The developments since his discovery have only served to demonstrate just how seminal it was. It remains a major tool in the subject and in surrounding areas. It is pertinent to note that a 1987 graduate text which aimed to describe the result and to survey some of its consequences ("Noncommutative Noetherian Rings" by J.C. McConnell and J.C. Robson) uses about 50 pages to establish Goldie's Theorem and over 500 pages to outline consequences.

Goldie had many able research students with whom he worked in a way which now, in these increasingly bureaucratic days, would be frowned upon. He suggested a potentially fruitful area for each to work in - and left them to it.

His distinguished work gained him the prestigious Senior Berwick Prize from the London Mathematical Society. He also served on its council and became its Vice-President, 1978-80. An international symposium marked his retirement, but he continued research, living in Bowness-on-Windermere.

Alfred Goldie was a very practical man, particularly enjoying working with wood. He also had a love of the outdoors, which he shared with his first wife, Mary, a geographer. Despite somewhat incompatible personalities, they still managed to give their three children a stable and happy upbringing. After Mary died in 1995, he married Margaret Turner.

**J. Chris Robson**

Published: 2 January 2006 © Independent