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Agata Smoktunowicz
Agata Smoktunowicz FRSE (born 12 October 1973) is a Polish mathematician who works as a professor at the University of Edinburgh. Her research is in abstract algebra.Agata Smoktunowicz , European Women in Mathematics, retrieved 31 December 2014.Currculum vitae , retrieved 31 December 2014. Contributions Smoktunowicz's contributions to mathematics include constructing nil rings, solving a "famous problem" formulated in 1 ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand–Kirillov Dimension
In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module ''M'' over a ''k''-algebra ''A'' is: :\operatorname = \sup_ \limsup_ \log_n \dim_k M_0 V^n where the supremum is taken over all finite-dimensional subspaces V \subset A and M_0 \subset M. An algebra is said to have ''polynomial growth'' if its Gelfand–Kirillov dimension is finite. Basic facts *The Gelfand–Kirillov dimension of a finitely generated commutative algebra ''A'' over a field is the Krull dimension of ''A'' (or equivalently the transcendence degree of the field of fractions of ''A'' over the base field.) *In particular, the GK dimension of the polynomial ring k _1, \dots, x_n/math> Is ''n''. *(Warfield) For any real number ''r'' ≥ 2, there exists a finitely generated algebra whose GK dimension is ''r''. In the theory of D-Modules Given a right module ''M'' over the Weyl algebra A_n, the Gelfand–Kirillov dimension of ''M'' over the Weyl algebra coincides with the dimension of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Algebra
''Journal of Algebra'' (ISSN 0021-8693) is an international mathematical research journal in algebra. An imprint of Academic Press, it is published by Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, .... ''Journal of Algebra'' was founded by Graham Higman, who was its editor from 1964 to 1984. From 1985 until 2000, Walter Feit served as its editor-in-chief. In 2004, ''Journal of Algebra'' announced (vol. 276, no. 1 and 2) the creation of a new section on computational algebra, with a separate editorial board. The first issue completely devoted to computational algebra was vol. 292, no. 1 (October 2005). The Editor-in-Chief of the ''Journal of Algebra'' is Michel Broué, Université Paris Diderot, and Gerhard Hiß, Rheinisch-Westfälische Technische Hochschule Aachen ( R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, San Diego
The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Established in 1960 near the pre-existing Scripps Institution of Oceanography in La Jolla, UC San Diego is the southernmost of the ten campuses of the University of California. It offers over 200 undergraduate and graduate degree programs, enrolling 33,096 undergraduate and 9,872 graduate students, with the second largest student housing capacity in the nation. The university occupies near the Pacific coast. UC San Diego consists of 12 undergraduate, graduate, and professional schools as well as 8 undergraduate residential colleges. The university operates 19 organized research units as well as 8 School of Medicine research units, 6 research centers at Scripps Institution of Oceanography, and 2 multi-campus initiatives. UC San Diego is als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University
Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United States, and one of the nine colonial colleges chartered before the American Revolution. Yale was established as the Collegiate School in 1701 by Congregationalism in the United States, Congregationalist clergy of the Connecticut Colony. Originally restricted to instructing ministers in theology and sacred languages, the school's curriculum expanded, incorporating humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first Doctor of Philosophy, PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew rapidly after 1890 due to the expansion of the physical campus and its scientif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excellence in research, teaching, and further education, which usually includes a dissertation. The degree, sometimes abbreviated ''Dr. habil''. (), ''dr hab.'' (), or ''D.Sc.'' ('' Doctor of Sciences'' in Russia and some CIS countries), is often a qualification for full professorship in those countries. In German-speaking countries it allows the degree holder to bear the title ''PD'' (for ). In a number of countries there exists an academic post of docent, appointment to which often requires such a qualification. The degree conferral is usually accompanied by a public oral defence event (a lecture or a colloquium) with one or more opponents. Habilitation is usually awarded 5–15 years after a PhD degree or its equivalent. Achieving this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow
A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, professional societies, the term refers to a privileged member who is specially elected in recognition of their work and achievements. Within institutions of higher education, a fellow is a member of a highly ranked group of teachers at a particular college or university or a member of the governing body in some universities. It can also be a specially selected postgraduate student who has been appointed to a post (called a fellowship) granting a stipend, research facilities and other privileges for a fixed period (usually one year or more) in order to undertake some advanced study or research, often in return for teaching services. In the context of medical education in North America, a fellow is a physician who is undergoing a supervised, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edinburgh Mathematical Society
The Edinburgh Mathematical Society is a mathematical society for academics in Scotland. History The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew Jeffrey Gunion Barclay FRSE, both maths teachers at George Watson's College, and Cargill Gilston Knott, the assistant of Peter Guthrie Tait, professor of physics at the University of Edinburgh. The first president, elected at first meeting on 2 February 1883, was J.S. Mackay, the head mathematics master at the Edinburgh Academy. The Society was founded at a time when mathematics societies were being created around the world, but it was unusual in being founded by school teachers rather than university lecturers. This was because, due to the very small number of mathematical academic positions in Scotland at the time, many skilled mathematics graduates chose to become schoolteachers instead. The fifty five founding members contained teac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of International Congresses Of Mathematicians Plenary And Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich *Jules Andrade *Léon Autonne *Émile Borel *Nikolai Bugaev *Francesco Brioschi *Hermann Brunn *Cesare Burali-Forti *Charles Jean de la Vallée Poussin *Gustaf Eneström *Federigo Enriques *Gino Fano *Zoel García de Galdeano *Francesco Gerbaldi *Paul Gordan *Jacques Hadamard *Adolf Hurwitz *Felix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Köthe Conjecture
In mathematics, the Köthe conjecture is a problem in ring theory, open . It is formulated in various ways. Suppose that ''R'' is a ring. One way to state the conjecture is that if ''R'' has no nil ideal, other than , then it has no nil one-sided ideal, other than . This question was posed in 1930 by Gottfried Köthe (1905–1989). The Köthe conjecture has been shown to be true for various classes of rings, such as polynomial identity rings and right Noetherian rings, but a general solution remains elusive. Equivalent formulations The conjecture has several different formulations: # (Köthe conjecture) In any ring, the sum of two nil left ideals is nil. # In any ring, the sum of two one-sided nil ideals is nil. # In any ring, every nil left or right ideal of the ring is contained in the upper nil radical of the ring. # For any ring ''R'' and for any nil ideal ''J'' of ''R'', the matrix ideal M''n''(''J'') is a nil ideal of M''n''(''R'') for every ''n''. # For any ring ''R'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers. Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings. A closely related notion is that of the ring of polynomial functions on a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nil Ideal
In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if all of its elements is nilpotent, i.e for each a \in I exists natural number ''n'' for which a^n = 0. If all elements of a ring is nilpotent (this is possible only for rings without a unit), then the ring is called a nil ring. , p. 194 The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nilpotent elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture. Commutative rings In commutative rings, the nil ideals are better understood than in noncommutative rings, primarily because in commutative rings, products involving nilpotent elements and sums of nilpotent elements are both nilpotent. This is because if ''a'' and ''b'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
