|
Alfred Loewy
Alfred Loewy (20 June 1873 – 25 January 1935) was a German mathematician who worked on representation theory. Loewy rings, Loewy length, Loewy decomposition and Loewy series are named after him. His graduate students included Wolfgang Krull and Friedrich Karl 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 .... Books *''Versicherungsmathematik'', 1903 *''Lehrbuch der Algebra'', 1915 *''Grundlagen der Arithmetik'' 1915''Mathematik des Geld- und Zahlungsverkehrs'' 1920 Notes References * * * Volker R. Remmert: Zur Mathematikgeschichte in Freiburg. Alfred Loewy (1873-1935): Jähes Ende späten Glanzes, in: Freiburger Universitätsblätter 129(1995), 81-102 20th-century German mathematicians 1873 births 1935 deaths People from Rawicz People from the Province of P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Loewy
Alfred Loewy (20 June 1873 – 25 January 1935) was a German mathematician who worked on representation theory. Loewy rings, Loewy length, Loewy decomposition and Loewy series are named after him. His graduate students included Wolfgang Krull and Friedrich Karl 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 .... Books *''Versicherungsmathematik'', 1903 *''Lehrbuch der Algebra'', 1915 *''Grundlagen der Arithmetik'' 1915''Mathematik des Geld- und Zahlungsverkehrs'' 1920 Notes References * * * Volker R. Remmert: Zur Mathematikgeschichte in Freiburg. Alfred Loewy (1873-1935): Jähes Ende späten Glanzes, in: Freiburger Universitätsblätter 129(1995), 81-102 20th-century German mathematicians 1873 births 1935 deaths People from Rawicz People from the Province of P ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loewy Ring
In mathematics, a Loewy ring or semi-Artinian ring is a ring in which every non-zero module has a non-zero socle, or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy. Loewy length The Loewy length and Loewy series were introduced by . If ''M'' is a module, then define the Loewy series ''M''α for ordinals α by ''M''0 = 0, ''M''α+1/''M''α = socle(''M''/''M''α), and ''M''α = ∪λ<α ''M''λ if α is a . The Loewy length of ''M'' is defined to be the smallest α with ''M'' = ''M''α, if it exists. Semiartinian modules is a semiartinian module if, for all |
Loewy Length
In mathematics, a Loewy ring or semi-Artinian ring is a ring in which every non-zero module has a non-zero socle, or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy. Loewy length The Loewy length and Loewy series were introduced by . If ''M'' is a module, then define the Loewy series ''M''α for ordinals α by ''M''0 = 0, ''M''α+1/''M''α = socle(''M''/''M''α), and ''M''α = ∪λ<α ''M''λ if α is a . The Loewy length of ''M'' is defined to be the smallest α with ''M'' = ''M''α, if it exists. Semiartinian modules is a semiartinian module if, for all |
Loewy Decomposition
In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy. Solving differential equations is one of the most important subfields in mathematics. Of particular interest are solutions in closed form. Breaking ODEs into largest irreducible components, reduces the process of solving the original equation to solving irreducible equations of lowest possible order. This procedure is algorithmic, so that the best possible answer for solving a reducible equation is guaranteed. A detailed discussion may be found in., F.Schwarz, Loewy Decomposition of Linear Differential Equations, Springer, 2012 Loewy's results have been extended to linear partial differential equations (PDEs) in two independent variables. In this way, algorithmic methods for solving large classes of linear PDEs have become available. Decomposing linear ordinary dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loewy Series
In mathematics, a Loewy ring or semi-Artinian ring is a ring in which every non-zero module has a non-zero socle, or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy. Loewy length The Loewy length and Loewy series were introduced by . If ''M'' is a module, then define the Loewy series ''M''α for ordinals α by ''M''0 = 0, ''M''α+1/''M''α = socle(''M''/''M''α), and ''M''α = ∪λ<α ''M''λ if α is a . The Loewy length of ''M'' is defined to be the smallest α with ''M'' = ''M''α, if it exists. Semiartinian modules is a semiartinian module if, for all |
Wolfgang Krull
Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden. He attended the Universities of Freiburg, Rostock and finally Göttingen from 1919–1921, where he earned his doctorate under Alfred Loewy. He worked as an instructor and professor at Freiburg, then spent a decade at the University of Erlangen. In 1939 Krull moved to become chair at the University of Bonn, where he remained for the rest of his life. Wolfgang Krull was a member of the Nazi Party. His 35 doctoral students include Wilfried Brauer, Karl-Otto Stöhr and Jürgen Neukirch. See also * Cohen structure theorem * Jacobson ring * Local ring * Prime ideal * Real algebraic geometry * Regular local ring * Valuation ring * Krull dimension * Krull ring * Krull topology * Krull–Azumaya theorem * Krull–Schmidt category * Krull–S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Karl 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1873 Births
Events January–March * January 1 ** Japan adopts the Gregorian calendar. ** The California Penal Code goes into effect. * January 17 – American Indian Wars: Modoc War: First Battle of the Stronghold – Modoc Indians defeat the United States Army. * February 11 – The Spanish Cortes deposes King Amadeus I, and proclaims the First Spanish Republic. * February 12 ** Emilio Castelar, the former foreign minister, becomes prime minister of the new Spanish Republic. ** The Coinage Act of 1873 in the United States is signed into law by President Ulysses S. Grant; coming into effect on April 1, it ends bimetallism in the U.S., and places the country on the gold standard. * February 20 ** The University of California opens its first medical school in San Francisco. ** British naval officer John Moresby discovers the site of Port Moresby, and claims the land for Britain. * March 3 – Censorship: The United States Congress enacts the Comstock Law, making it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1935 Deaths
Events January * January 7 – Italian premier Benito Mussolini and French Foreign Minister Pierre Laval conclude an agreement, in which each power agrees not to oppose the other's colonial claims. * January 12 – Amelia Earhart becomes the first person to successfully complete a solo flight from Hawaii to California, a distance of 2,408 miles. * January 13 – A plebiscite in the Territory of the Saar Basin shows that 90.3% of those voting wish to join Germany. * January 24 – The first canned beer is sold in Richmond, Virginia, United States, by Gottfried Krueger Brewing Company. February * February 6 – Parker Brothers begins selling the board game Monopoly in the United States. * February 13 – Richard Hauptmann is convicted and sentenced to death for the kidnapping and murder of Charles Lindbergh Jr. in the United States. * February 15 – The discovery and clinical development of Prontosil, the first broadly effective antibiotic, is published in a se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
