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Alfred Goldie
Alfred William Goldie (10 December 1920, Coseley, Staffordshire – 8 October 2005, Barrow-in-Furness, Cumbria) was an English mathematician. Biography Goldie was educated at Wolverhampton Grammar School and then read mathematics at St John's College, Cambridge. His studies were interrupted by war work on ballistics with the Armament Research Department of the Ministry of Supply, eventually taking his BA in 1942 and MA in 1946. Academic career Goldie became an assistant lecturer at the University of Nottingham in 1946. In 1948 he was appointed lecturer in Pure Mathematics at what was then King's College, Durham (and has been the University of Newcastle upon Tyne since 1963) where he was promoted to senior lecturer in 1958 and reader in algebra in 1960. In 1963 Goldie was appointed Professor of Pure Mathematics at the University of Leeds. He retired from his chair in 1986 with the title emeritus professor. Goldie won the 1970 Senior Berwick Prize from the London Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staffordshire
Staffordshire (; postal abbreviation Staffs.) is a landlocked county in the West Midlands region of England. It borders Cheshire to the northwest, Derbyshire and Leicestershire to the east, Warwickshire to the southeast, the West Midlands County and Worcestershire to the south and Shropshire to the west. The largest settlement in Staffordshire is Stoke-on-Trent, which is administered as an independent unitary authority, separately from the rest of the county. Lichfield is a cathedral city. Other major settlements include Stafford, Burton upon Trent, Cannock, Newcastle-under-Lyme, Rugeley, Leek, and Tamworth. Other towns include Stone, Cheadle, Uttoxeter, Hednesford, Brewood, Burntwood/Chasetown, Kidsgrove, Eccleshall, Biddulph and the large villages of Penkridge, Wombourne, Perton, Kinver, Codsall, Tutbury, Alrewas, Barton-under-Needwood, Shenstone, Featherstone, Essington, Stretton and Abbots Bromley. Cannock Chase AONB is within the county as well as parts of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newcastle University
Newcastle University (legally the University of Newcastle upon Tyne) is a UK public university, public research university based in Newcastle upon Tyne, North East England. It has overseas campuses in Singapore and Malaysia. The university is a red brick university and a member of the Russell Group, an association of research-intensive UK universities. The university finds its roots in the School of Medicine and Surgery (later the College of Medicine), established in 1834, and the Edward Fenwick Boyd#College of Physical Science, College of Physical Science (later renamed Armstrong College), founded in 1871. These two colleges came to form the larger division of the federal University of Durham, with the Durham Colleges forming the other. The Newcastle colleges merged to form King's College in 1937. In 1963, following an Act of Parliament, King's College became the University of Newcastle upon Tyne. The university subdivides into three faculties: the Faculty of Humanities and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 over itself, and satisfies the ascending chain condition on right annihilators of subsets of ''R''. Goldie's theorem states that the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients is then completely determined by the Artin–Wedderburn theorem. In particular, Goldie's theorem applies to semiprime right Noetherian rings, since by definition right Noetherian rings have the ascending chain condition on ''all'' right ideals. This is sufficient to guarantee that a right-Noetherian ring is right Goldie. The converse does not hold: every right Ore domain is a right Goldie domain, and hence so is every commutative integral domain. A con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Module
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) uniform ring if it is uniform as a right (left) module over itself. Alfred Goldie used the notion of uniform modules to construct a measure of dimension for modules, now known as the uniform dimension (or Goldie dimension) of a module. Uniform dimension generalizes some, but not all, aspects of the notion of the dimension of a vector space. Finite uniform dimension was a key assumption for several theorems by Goldie, including Goldie's theorem, which characterizes which rings are right orders in a semisimple ring. Modules of finite uniform dimension generalize both Artinian modules and Noetherian modules. In the literature, uniform dimension is also referred to as simply the dimension of a module or the rank of a module. Uniform dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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) uniform ring if it is uniform as a right (left) module over itself. Alfred Goldie used the notion of uniform modules to construct a measure of dimension for modules, now known as the uniform dimension (or Goldie dimension) of a module. Uniform dimension generalizes some, but not all, aspects of the notion of the dimension of a vector space. Finite uniform dimension was a key assumption for several theorems by Goldie, including Goldie's theorem, which characterizes which rings are right orders in a semisimple ring. Modules of finite uniform dimension generalize both Artinian modules and Noetherian modules. In the literature, uniform dimension is also referred to as simply the dimension of a module or the rank of a module. Uniform dim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Theory
In algebra, ring theory is the study of rings— algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological algebra, homological properties and Polynomial identity ring, polynomial identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of ''commutative algebra'', a major area of modern mathematics. Because these three fields (algebraic geometry, alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senior 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 society to establish two prizes. His widow Daisy May Berwick gave the society the money and the society established the prizes, with the first Senior Berwick Prize being presented in 1946 and the first Junior Berwick Prize the following year. The prizes are awarded "in recognition of an outstanding piece of mathematical research ... published by the Society" in the eight years before the year of the award. The Berwick Prize was known as the Junior Berwick Prize up to 1999, and was given its current name for the 2001 award. Senior Berwick Prize winners Source:List of LMS prize winners L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title the rank of the last office held". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished service awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title, e.g., "professor emeritus". The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In the description of deceased professors emeritus listed at U.S. universities, the title ''emeritus'' is replaced by indicating the years of their appointmentsThe Protoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Leeds
, mottoeng = And knowledge will be increased , established = 1831 – Leeds School of Medicine1874 – Yorkshire College of Science1884 - Yorkshire College1887 – affiliated to the federal Victoria University1904 – University of Leeds , type = Public , endowment = £90.5 million , budget = £751.7 million , chancellor = Jane Francis , vice_chancellor = Simone Buitendijk , students = () , undergrad = () , postgrad = () , city = Leeds , province = West Yorkshire , country = England , campus = Urban, suburban , free_label = Newspaper , free = The Gryphon , colours = , website www.leeds.ac.uk, logo = Leeds University logo.svg , logo_size = 250 , administrative_staff = 9,200 , coor = , affiliations = 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 renam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors are usually experts in their field and teachers of the highest rank. In most systems of List of academic ranks, academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor". In some countries and institutions, the word "professor" is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the unqualified word is also used colloquially to refer to associate and assistant professors as well. This usage would be considered incorrect among other academic communities. However, the otherwise unqualified title "Professor" designated with a capital let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
