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).
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.
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.
BucraniumBucranium (plural bucrania; Latin, from Greek βουκράνιον, referring to the skull of an ox) was a form of carved decoration commonly used in Classical architecture. The name is generally considered to originate with the practice of displaying garlanded, sacrificial oxen, whose heads were displayed on the walls of temples, a practice dating back to the sophisticated Neolithic site of Çatalhöyük in eastern Anatolia, where cattle skulls were overlaid with white plaster.
NantesNantes (nɒ̃t, USalsonɑːnt(s), nɑ̃t; Gallo: Naunnt or Nantt nɑ̃(ː)t; Naoned ˈnãunət) is a city in Loire-Atlantique on the Loire, from the Atlantic coast. The city is the sixth largest in France, with a population of 320,732 in Nantes proper and a metropolitan area of nearly 1 million inhabitants (2020). With Saint-Nazaire, a seaport on the Loire estuary, Nantes forms one of the main north-western French metropolitan agglomerations. It is the administrative seat of the Loire-Atlantique department and the Pays de la Loire region, one of 18 regions of France.
