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F. K. Schmidt
Friedrich Karl Schmidt (22 September 1901 – 25 January 1977) was a German mathematician, who made notable contributions to algebra and number theory. Schmidt studied from 1920 to 1925 in Freiburg and Marburg. In 1925 he completed his doctorate at the Albert-Ludwigs-Universität Freiburg under the direction of Alfred Loewy. In 1927 he became a ''Privatdozent'' (lecturer) at the University of Erlangen, where he received his habilitation and in 1933 became a professor extraordinarius. In 1933/34 he was a ''Dozent'' at the University of Göttingen, where he worked with Helmut Hasse. Schmidt was then a professor ordinarius at the University of Jena from 1934 to 1945. During WW II, he was at the ''Deutsche Versuchsanstalt für Segelflug'' (German Research Station for Gliding) in Reichenhall. He was a professor from 1946 to 1952 at Westfälischen Wilhelms-Universität in Münster and from 1952 to 1966 at the University of Heidelberg, where he retired as professor emeritus. In the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Düsseldorf
Düsseldorf ( , , ; often in English sources; Low Franconian and Ripuarian: ''Düsseldörp'' ; archaic nl, Dusseldorp ) is the capital city of North Rhine-Westphalia, the most populous state of Germany. It is the second-largest city in the state and the seventh-largest city in Germany, with a population of 617,280. Düsseldorf is located at the confluence of two rivers: the Rhine and the Düssel, a small tributary. The ''-dorf'' suffix means "village" in German (English cognate: ''thorp''); its use is unusual for a settlement as large as Düsseldorf. Most of the city lies on the right bank of the Rhine. Düsseldorf lies in the centre of both the Rhine-Ruhr and the Rhineland Metropolitan Region. It neighbours the Cologne Bonn Region to the south and the Ruhr to the north. It is the largest city in the German Low Franconian dialect area (closely related to Dutch). Mercer's 2012 Quality of Living survey ranked Düsseldorf the sixth most livable city in the world. Düsse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfer o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Field
In algebra, a field ''k'' is perfect if any one of the following equivalent conditions holds: * Every irreducible polynomial over ''k'' has distinct roots. * Every irreducible polynomial over ''k'' is separable. * Every finite extension of ''k'' is separable. * Every algebraic extension of ''k'' is separable. * Either ''k'' has characteristic 0, or, when ''k'' has characteristic , every element of ''k'' is a ''p''th power. * Either ''k'' has characteristic 0, or, when ''k'' has characteristic , the Frobenius endomorphism is an automorphism of ''k''. * The separable closure of ''k'' is algebraically closed. * Every reduced commutative ''k''-algebra ''A'' is a separable algebra; i.e., A \otimes_k F is reduced for every field extension ''F''/''k''. (see below) Otherwise, ''k'' is called imperfect. In particular, all fields of characteristic zero and all finite fields are perfect. Perfect fields are significant because Galois theory over these fields becomes simpler, since the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann–Roch Theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus ''g'', in a way that can be carried over into purely algebraic settings. Initially proved as Riemann's inequality by , the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student . It was later generalized to algebraic curves, to higher-dimensional varieties and beyond. Preliminary notions A Riemann surface X is a topological space that is locally homeomorphic to an open subset of \Complex, the set of complex numbers. In addition, the transition maps between these open subsets are required to be holomorphic. The latter condition allows one to transfer the notions and methods of complex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Function Field
In mathematics, an algebraic function field (often abbreviated as function field) of ''n'' variables over a field ''k'' is a finitely generated field extension ''K''/''k'' which has transcendence degree ''n'' over ''k''. Equivalently, an algebraic function field of ''n'' variables over ''k'' may be defined as a finite field extension of the field ''K'' = ''k''(''x''1,...,''x''''n'') of rational functions in ''n'' variables over ''k''. Example As an example, in the polynomial ring ''k'' 'X'',''Y''consider the ideal generated by the irreducible polynomial ''Y''2 − ''X''3 and form the field of fractions of the quotient ring ''k'' 'X'',''Y''(''Y''2 − ''X''3). This is a function field of one variable over ''k''; it can also be written as k(X)(\sqrt) (with degree 2 over k(X)) or as k(Y)(\sqrt (with degree 3 over k(Y)). We see that the degree of an algebraic function field is not a well-defined notion. Category structure The algebraic function fields over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeta Function
In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * Arakawa–Kaneko zeta function * Arithmetic zeta function * Artin–Mazur zeta function of a dynamical system * Barnes zeta function or double zeta function * Beurling zeta function of Beurling generalized primes * Dedekind zeta function of a number field * Duursma zeta function of error-correcting codes * Epstein zeta function of a quadratic form * Goss zeta function of a function field * Hasse–Weil zeta function of a variety * Height zeta function of a variety * Hurwitz zeta function, a generalization of the Riemann zeta function * Igusa zeta function * Ihara zeta function of a graph * ''L''-function, a "twisted" zeta function * Lefschetz zeta function of a morphism * Lerch zeta function, a generalization of the Riemann zeta function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free University Of Berlin
The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and the humanities. It is recognised as a leading university in international university rankings. The Free University of Berlin was founded in West Berlin in 1948 with American support during the early Cold War period as a Western continuation of the Friedrich Wilhelm University, or the University of Berlin, whose traditions and faculty members it retained. The Friedrich Wilhelm University (which was renamed the Humboldt University), being in East Berlin, faced strong communist repression; the Free University's name referred to West Berlin's status as part of the Western Free World, in contrast to communist-controlled East Berlin. In 2008, as part of a joint effort, the Free University of Berlin, along with the Hertie School of Governance, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heidelberger Akademie Der Wissenschaften
The Heidelberg Academy of Sciences and Humanities (German: ''Heidelberger Akademie der Wissenschaften''), established in 1909 in Heidelberg, Germany, is an assembly of scholars and scientists in the German state of Baden-Wuerttemberg. The Academy is a member of the Union of German Academies of Sciences and Humanities The Union of German Academies of Sciences and Humanities (German: Union der deutschen Akademien der Wissenschaften) is an umbrella organisation for eight German academies of sciences and humanities. The member academies are: *Berlin-Brandenburg Ac .... References External linksHeidelberg Academy of Sciences and Humanities website 1909 establishments in Germany Scientific organizations established in 1909 Union of German Academies of Sciences and Humanities Education in Heidelberg {{Germany-org-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Heidelberg
} Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest university and one of the world's oldest surviving universities; it was the third university established in the Holy Roman Empire. Heidelberg is one of the most prestigious and highly ranked universities in Europe and the world. Heidelberg has been a coeducational institution since 1899. The university consists of twelve faculties and offers degree programmes at undergraduate, graduate and postdoctoral levels in some 100 disciplines. The language of instruction is usually German, while a considerable number of graduate degrees are offered in English as well as some in French. As of 2021, 57 Nobel Prize winners have been affiliated with the city o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reichenhall
Bad Reichenhall (Central Bavarian: ''Reichahoi'') is a spa town, and administrative center of the Berchtesgadener Land district in Upper Bavaria, Germany. It is located near Salzburg in a basin encircled by the Chiemgau Alps (including Mount Staufen (1,771 m) and Mount Zwiesel (1,781 m)). Together with other alpine towns Bad Reichenhall engages in the Alpine Town of the Year Association for the implementation of the Alpine Convention to achieve sustainable development in the alpine arc. Bad Reichenhall was awarded Alpine Town of the Year in 2001. Bad Reichenhall is a traditional center of salt production, obtained by evaporating water saturated with salt from brine ponds. History * The earliest known inhabitants of this area are the tribes of the Glockenbecher-Culture (a Bronze Age Culture, from about 2000 B.C.) * In the age of the La Tene culture (about 450 B.C.) organised salt production commenced utilising the local brine pools. In the same period a Celtic place of worship i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
