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Anton Sushkevich
Anton Kazimirovich Sushkevich (Антон Казимирович Сушкевич) (23 January 1889, Borisoglebsk, Russia — 30 August 1961, Kharkiv, Ukraine) was a Russian mathematician and textbook author who expanded group theory to include semigroups and other magmas. Sushkevich attended secondary school in Voronezh and studied in Berlin from 1906 to 1911. There he attended lectures of F. G. Frobenius, Issai Schur, and Hermann Schwarz. Sushkevich studied piano with L. V. Rostropovich, father of Mstislav Rostropovich. In 1906 he was a cello student at Stern Conservatory (now part of Berlin University of the Arts). In 1911 he moved to Saint Petersburg, graduating from the Imperial University in 1913. Moving to Kharkiv, Suskevich taught in secondary education while he pursued a graduate degree at Kharkov State University. His dissertation was ''The theory of operations as the general theory of groups''. Obtaining the degree, he became an assistant professor at the university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borisoglebsk
Borisoglebsk (russian: Борисогле́бск) is a town in Voronezh Oblast, Russia, located on the left bank of the Vorona River near its confluence with the Khopyor. Population: 65,000 (1969). History Borisoglebsk was founded in 1646 and was named for the Russian saints Boris and Gleb, the first saints canonized in Kievan Rus' after the Christianization of the country. In the late 19th century and the early 20th century Borisoglebsk developed into a busy inland port due to its geographic location within the highly fertile Central Black Earth Region. Barges transported good such as grain, timber, kerosene, fish, eggs, watermelon from the region to large cities in western and central Russia connected to Borisoglebsk by waterways such as St. Petersburg, Moscow, Rostov, Taganrog, and Tsaritsyn. In 1870, a brewer plant opened in the town, producing dark beer and light beer, as well as fruit soda. The brewery has survived and continues to produce beer. According to the 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin University Of The Arts
The Universität der Künste Berlin (UdK; also known in English as the Berlin University of the Arts), situated in Berlin, Germany, is the largest art school in Europe. It is a public art and design school, and one of the four research universities in the city. The university is known for being one of the biggest and most diversified universities of the arts worldwide. It has four colleges specialising in fine arts, architecture, media and design, music and the performing arts with around 3,500 students. Thus the UdK is one of only three universities in Germany to unite the faculties of art and music in one institution. The teaching offered at the four colleges encompasses the full spectrum of the arts and related academic studies in more than 40 courses. Having the right to confer doctorates and post-doctoral qualifications, Berlin University of the Arts is also one of Germany's few art colleges with full university status. Outstanding professors and students at all its colleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ''ring'' is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ''ring'' is an abelian group whose operation is called ''addition'', with a second binary operation called ''multiplication'' that is associative, is distributive over the addition operation, and has a multiplicative identity element. (Some authors use the term " " with a missing i to refer to the more general structure that omits this last requirement; see .) Whether a ring is commutative (that is, whether the order in which two elements are multiplied might change the result) has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Domain
In mathematics, specifically abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain, every nonzero element ''a'' has the cancellation property, that is, if , an equality implies . "Integral domain" is defined almost universally as above, but there is some variation. This article follows the convention that rings have a multiplicative identity, generally denoted 1, but some authors do not follow this, by not requiring integral domains to have a multiplicative identity. Noncommutative integral domains are sometimes admitted. This article, however, follows the much more usual convention of reserving the term "integral domain" for the commutative case and using "domain" for the general case including noncommutative rings. Some sources, notably Lang, use the term entir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and ''p''-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holodomor
The Holodomor ( uk, Голодомо́р, Holodomor, ; derived from uk, морити голодом, lit=to kill by starvation, translit=moryty holodom, label=none), also known as the Terror-Famine or the Great Famine, was a man-made famine in Soviet Ukraine from 1932 to 1933 that killed millions of Ukrainians. The Holodomor was part of the wider Soviet famine of 1932–1933 which affected the major grain-producing areas of the Soviet Union. While scholars universally agree that the cause of the famine was man-made, whether the Holodomor constitutes a genocide remains in dispute. Some historians conclude that the famine was planned and exacerbated by Joseph Stalin in order to eliminate a Ukrainian independence movement. This conclusion is supported by Raphael Lemkin. Others suggest that the famine arose because of rapid Soviet industrialisation and collectivization of agriculture. Ukraine was one of the largest grain-producing states in the USSR and was subject to unre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Famine
A famine is a widespread scarcity of food, caused by several factors including war, natural disasters, crop failure, Demographic trap, population imbalance, widespread poverty, an Financial crisis, economic catastrophe or government policies. This phenomenon is usually accompanied or followed by regional malnutrition, starvation, epidemic, and increased death, mortality. Every inhabited continent in the world has experienced a period of famine throughout history. In the 19th and 20th century, generally characterized Southeast and South Asia, as well as Eastern and Central Europe, in terms of having suffered most number of deaths from famine. The numbers dying from famine began to fall sharply from the 2000s. Since 2010, Africa has been the most affected continent of famine in the world. Definitions According to the United Nations World Food Programme, famine is declared when malnutrition is widespread, and when people have started dying of starvation through lack of access to suf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matematicheskii Sbornik
''Matematicheskii Sbornik'' (russian: Математический сборник, abbreviated ''Mat. Sb.'') is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866. It is the oldest successful Russian mathematical journal. The English translation is ''Sbornik: Mathematics''. It is also sometimes cited under the alternative name ''Izdavaemyi Moskovskim Matematicheskim Obshchestvom'' or its French translation ''Recueil mathématique de la Société mathématique de Moscou'', but the name ''Recueil mathématique'' is also used for an unrelated journal, '' Mathesis''. Yet another name, ''Sovetskii Matematiceskii Sbornik'', was listed in a statement in the journal in 1931 apologizing for the former editorship of Dmitri Egorov, who had been recently discredited for his religious views; however, this name was never actually used by the journal. The first editor of the journal was Nikolai Brashman, who died before its first issue (dedicated to hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley's Theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group is isomorphic to a subgroup of a symmetric group. More specifically, is isomorphic to a subgroup of the symmetric group \operatorname(G) whose elements are the permutations of the underlying set of . Explicitly, * for each g \in G, the left-multiplication-by- map \ell_g \colon G \to G sending each element to is a permutation of , and * the map G \to \operatorname(G) sending each element to \ell_g is an injective homomorphism, so it defines an isomorphism from onto a subgroup of \operatorname(G). The homomorphism G \to \operatorname(G) can also be understood as arising from the left translation action of on the underlying set . When is finite, \operatorname(G) is finite too. The proof of Cayley's theorem in this case shows that if is a finite group of order , then is isomorphic to a subgroup of the standard symmetric group S_n. But might also be isomorphic to a subgroup o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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