**Alfred Goldie** was an English mathematician who proved an important result in Ring Theory.

- Alfred attended Wolverhampton Grammar School where he won a scholarship to St John's College, Cambridge.
- Snow realised that, despite Goldie's training in the Officers Training Corps, he would make a more valuable contribution to the war effort using his mathematical skills in Ballistic Research.
- Goldie requested that he be allowed to begin studies for a Ph.D. at London University, and he was allowed to take some time off from his work at Woolwich Arsenal to undertake mathematical research.
- Since he wanted to undertake research in algebra, Goldie was advised to write to Hall seeking advice.
- This was readily given, and Hall suggested that Goldie read van der Waerden's Moderne Algebra, a difficult task for someone who did not speak German, but with the help of a dictionary Goldie soon mastered this fundamental text largely based on Emmy Noether's revolutionary contributions to algebra.
- Goldie continued to work at Woolwich Arsenal for another year, only leaving in September 1946 when he was appointed Assistant Lecturer in Mathematics at Nottingham University.
- This led Goldie to the results in universal algebra which he published in The Jordan-Hölder theorem for general abstract algebras (1950) and The scope of the Jordan-Hölder theorem in abstract algebra (1952).
- Kurt Hirsch was appointed to a Readership while Frank Bonsall and Alfred Goldie were appointed to Lectureships.
- Hirsch advised Goldie to concentrate on an area of algebra other than universal algebra, so he decided that ring theory would provide a good area which would complement the active UK research area of group theory which was led by Philip Hall.
- Thus it is not really surprising that Goldie's early work in ring theory was influenced by Jacobson's papers and books.
- Jacobson and Goldie had met at the International Congress of Mathematicians in Amsterdam in 1954 and at that time Jacobson suggested that Goldie work on problems in Notherian rings.
- Goldie's first paper in this area Decompositions of semi-simple rings (1956) made an immediate impact since Jacobson included one of Goldie's theorems in his classic monograph Structure of Rings of 1956, acknowledging that it had been communicated by Goldie.
- Over the next few years Goldie's work on non-commutative Notherian rings would totally revolutionise the subject.
- On one of these occasions, Goldie showed Brauer his result on Noetherian domains.
- Goldie published his results, now known as "Goldie's Theorem," in The structure of prime rings with maximum conditions (1958) and The structure of prime rings under ascending chain conditions (1958).
- 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 been promoted to Senior Lecturer at Newcastle, then in 1963 he was appointed Professor of Pure Mathematics at Leeds University.
- Goldie visited the U.S. many times, with extended stays at Yale, Tulane, and the University of California at San Diego.
- Among the honours Goldie received for his outstanding contributions, we mention the Senior Berwick Prize from the London Mathematical Society in 1970.
- Alfred Goldie was a very practical man, particularly enjoying working with wood.

Born 10 December 1920, Coseley, Staffordshire, England. Died 8 October 2005, Barrow in Furness, Cumbria, England.

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Origin England

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive