Abelian extensionIn abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.
Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
Separable extensionIn field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more general definition that applies when E is not necessarily algebraic over F. An extension that is not separable is said to be inseparable.
Art NouveauArt Nouveau (ˌɑːr(t)_nuːˈvoʊ , aʁ nuvo; "New Art") is an international style of art, architecture, and applied art, especially the decorative arts. It was often inspired by natural forms such as the sinuous curves of plants and flowers. Other characteristics of Art Nouveau were a sense of dynamism and movement, often given by asymmetry or whiplash lines, and the use of modern materials, particularly iron, glass, ceramics and later concrete, to create unusual forms and larger open spaces.
Group extensionIn mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If and are two groups, then is an extension of by if there is a short exact sequence If is an extension of by , then is a group, is a normal subgroup of and the quotient group is isomorphic to the group . Group extensions arise in the context of the extension problem, where the groups and are known and the properties of are to be determined.
Normal extensionIn abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K which has a root in L, splits into linear factors in L. These are one of the conditions for algebraic extensions to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. Let be an algebraic extension (i.e. L is an algebraic extension of K), such that (i.e. L is contained in an algebraic closure of K).
Art DecoArt Deco, short for the French Arts Décoratifs, and sometimes referred to simply as Deco, is a style of visual arts, architecture, and product design, that first appeared in France in the 1910s (just before World War I), and flourished in the United States and Europe during the 1920s to early 1930s. Through styling and design of the exterior and interior of anything from large structures to small objects, including how people look (clothing, fashion and jewelry), Art Deco has influenced bridges, buildings (from skyscrapers to cinemas), ships, ocean liners, trains, cars, trucks, buses, furniture, and everyday objects like radios and vacuum cleaners.
NeoclassicismNeoclassicism (also spelled Neo-classicism) was a Western cultural movement in the decorative and visual arts, literature, theatre, music, and architecture that drew inspiration from the art and culture of classical antiquity. Neoclassicism was born in Rome largely thanks to the writings of Johann Joachim Winckelmann, at the time of the rediscovery of Pompeii and Herculaneum, but its popularity spread across Europe as a generation of European art students finished their Grand Tour and returned from Italy to their home countries with newly rediscovered Greco-Roman ideals.
MarseilleMarseille (mɑːrˈseɪ , maʁsɛj, maχˈsɛjə; also spelled in English as Marseilles) is the prefecture of the French department of Bouches-du-Rhône and capital of the Provence-Alpes-Côte d'Azur region. Situated in the Provence region of southern France, it is located on the coast of the Gulf of Lion, part of the Mediterranean Sea, near the mouth of the Rhône river. Its occupants are called Marseillais.. Marseille is the second most populous city in France, with 870,321 inhabitants in 2020 (Jan.
Controlled-access highwayA controlled-access highway is a type of highway that has been designed for high-speed vehicular traffic, with all traffic flow—ingress and egress—regulated. Common English terms are freeway, motorway and expressway. Other similar terms include throughway (or thruway) and parkway. Some of these may be limited-access highways, although this term can also refer to a class of highways with somewhat less isolation from other traffic. In countries following the Vienna convention, the motorway qualification implies that walking and parking are forbidden.
