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concept and abelian
* ' Tohoku ': The approach in a celebrated paper by Alexander Grothendieck which appeared in the Second Series of the Tohoku Mathematical Journal in 1957, using the abelian category concept ( to include sheaves of abelian groups ).
There was perhaps a more direct route available: the abelian category concept had been introduced by Grothendieck in his foundational work on homological algebra, to unify categories of sheaves of abelian groups, and of modules.
* Regular p-group, a concept capturing some of the more important properties of abelian p-groups, but general enough to include most " small " p-groups.
To extend this to the case of an abelian variety A, André Weil had to make more explicit the way of quantifying the size of a solution, by means of a height function – a concept that became foundational.
* Topological abelian group, a concept in mathematics
This divisible group D is the injective envelope of A, and this concept is the injective hull in the category of abelian groups.
In early 1954, Chen Ning Yang and Robert Mills extended the concept of gauge theory for abelian groups, e. g. quantum electrodynamics, to nonabelian groups to provide an explanation for strong interactions.
In more abstract and geometric language, it is contained in the concept of abelian variety, or more precisely in the way an algebraic curve can be mapped into abelian varieties.
In the case of G an abelian variety it presents a technical obstacle, though it is known that the concept is potentially useful in connection with Tamagawa numbers.

concept and group
Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.
As a group they should be favorable to a concept of gradual Germanic infiltration although the specialist nature of much of their work, e.g. Seebohm, Gray and Finberg, tends to obscure their sympathies.
In Japan, because of intermarriage over many years with Japanese, the concept of a pure Ainu ethnic group is no longer feasible.
" An abstraction " is the product of this process – a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.
Basic constructions, such as the fundamental group or fundamental groupoid of a topological space, can be expressed as fundamental functors to the category of groupoids in this way, and the concept is pervasive in algebra and its applications.
* Class ( philosophy ), an analytical concept used differently to group phenomena from grouping as ' types ' or ' kinds '
Sorrow ( released in December 1968 ) by British group the Pretty Things is generally considered to be among the first creatively successful rock concept albums-in that each song is part of an overarching unified conceptthe life story of the main character, Sebastian Sorrow.
In the 1970s and 80s, The Alan Parsons Project was a British progressive rock group which specialized entirely in concept albums.
The British group A Flock of Seagulls, released their self-titled concept album based on an alien invasion.
The comedy group Buckner & Garcia released a novelty concept album, Pac-Man Fever, that went gold and produced a hit single of the same name ; all of the songs on the album pertained to popular video games of the time.
In 2004 the British hip hop group The Streets released A Grand Don't Come for Free, a concept album charting a period of the protagonists life in which he meets a girl, starts a relationship with her and then breaks up with her after finding out she has been cheating on him.
Jeff Lynne, frontman of fellow Birmingham group The Idle Race, was excited by the concept.
Historically, the concept of fundamental group first emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Henri Poincaré and Felix Klein, where it describes the monodromy properties of complex functions, as well as providing a complete topological classification of closed surfaces.
While Fascism claimed that corporatism gave workers power alongside employer in workplaces in reality the concept of " Fuhrerprinzip " gave employers and State-appointed workplace managers absolute control over the workplace as dictated by the State-owned German Labor Front ; based on the Social Darwinist ideology that certain individuals are " gifted " and " born to rule ", employers thought to be part of that group.
The concept of furry originated at a science fiction convention in 1980, when a drawing of a character from Steve Gallacci ’ s Albedo Anthropomorphics initiated a discussion of anthropomorphic characters in science fiction novels, which in turn initiated a discussion group that met at science fiction and comics conventions.
Federalism is a political concept in which a group of members are bound together by covenant ( Latin: foedus, covenant ) with a governing representative head.
country of origin and native land ) is the concept of the place ( cultural geography ) to which an ethnic group holds a long history and a deep cultural association withthe country in which a particular national identity began.
The term is credited to Wayne Hodgins when he created a working group in 1994 bearing the name though the concept was first described by Gerard in 1967.
The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s.
China covers a large geographic area and uses the concept of " Zhonghua minzu " or Chinese nationality, in the sense of ethnic groups, but it also officially recognizes the majority Han ethnic group which accounts for over 90 % of the population, and no fewer than 55 ethnic national minorities.
Israel's definition of a nation state differs from other countries as its concept of a nation state is based on the Ethnoreligious group ( Judaism ) rather than solely on ethnicity, while the ancient mother language of the Jews, Hebrew, was revived as a unifying bond between them as a national and official language.
To form a concept, one mentally isolates a group of concretes ( of distinct perceptual units ), on the basis of observed similarities which distinguish them from all other known concretes ( similarity is ' the relationship between two or more existents which possess the same characteristic ( s ), but in different measure or degree '); then, by a process of omitting the particular measurements of these concretes, one integrates them into a single new mental unit: the concept, which subsumes all concretes of this kind ( a potentially unlimited number ).

concept and is
A concept of responsibility is in process of articulation and establishment.
National responsibility for individual welfare is a concept not limited to the United States or even to the Western nations.
Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.
Whether a concept analogous to the principle of internal responsibility operates in a nation's external relations is less obvious and more difficult to establish.
) The concept of nationalism is the political principle that epitomizes and glorifies the territorial state as the characteristic type of socal structure.
But it is more than irony: one of the main reasons why nationalism is no longer a tenable concept is because it has spread throughout the planet.
It is interesting, however, that despite this strong upsurge in Southern writing, almost none of the writers has forsaken the firmly entrenched concept of the white-suited big-daddy colonel sipping a mint julep as he silently recounts the revenue from the season's cotton and tobacco crops ; ;
A broader concept of imitation is needed, one which acknowledges that true invention is important, that the artist's creativity in part transcends the non-artistic causal factors out of which it arises.
Who will deny that in a vast portion of the South the Federal action is incompatible with the Jeffersonian concept of `` the consent of the governed ''??
For it is their catastrophic concept of the Anglo-Saxon invasions rather than Kemble's gradualist approach which dominates the field.
But beginning, for all practical purposes, with Frederick Seebohm's English Village Community scholars have had to reckon with a theory involving institutional and agrarian continuity between Roman and Anglo-Saxon times which is completely at odds with the reigning concept of the Anglo-Saxon invasions.
It is ironic that Washington is having to struggle so for a concept that for six years it bypassed as unreasonable.
The concept of labor as a special class is outmoded, and in the task confronting America as bastion of the free world, labor must learn to put the national interest first if it is itself to survive.
The most fundamental concept of the new approach to economic aid is the focusing of our attention, our resources, and our energies on the effort to promote the economic and social development of the less developed countries.
While it is easy enough to ridicule Hawkins' pronouncement in Pleas Of The Crown from a metaphysical point of view, the concept of the `` oneness '' of a married couple may reflect an abiding belief that the communion between husband and wife is such that their actions are not always to be regarded by the criminal law as if there were no marriage.
That we had the wit and wisdom to adopt Mr. Lowell's concept and make it the base for our processes of selection is one reason why our selections have been, it may be said truly, pretty uniformly good.
It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.
The concept of trans-illumination ( as shown by the photo on p. 92 ), as just one example, offers an entirely new approach to lighting problems -- no matter what industry is involved.

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