Free moduleIn mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S. A free abelian group is precisely a free module over the ring Z of integers.
Module (mathematics)In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.
Projective moduleIn mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. Every free module is a projective module, but the converse fails to hold over some rings, such as Dedekind rings that are not principal ideal domains.
ViscosityThe viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square metre, or pascal-seconds. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion.
Cyclic moduleIn mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z-module) that is generated by one element. A left R-module M is called cyclic if M can be generated by a single element i.e. M = (x) = Rx = {rx r ∈ R} for some x in M. Similarly, a right R-module N is cyclic if N = yR for some y ∈ N. 2Z as a Z-module is a cyclic module.
Christian ClavierChristian Jean-Marie Clavier (kʁistjɑ̃ ʒɑ̃ maʁi klavje; born 6 May 1952) is a French actor, screenwriter, film producer and director. He became widely popular after starring in two hit comedy series: Patrice Leconte's Les Bronzés and Les Visiteurs directed by Jean-Marie Poiré. He furthered his popularity by taking a role of Asterix in the screen adaptations of the comic books by Albert Uderzo and René Goscinny. He is the brother of French film director Stéphane Clavier.
1973 in FranceEvents from the year 1973 in France. President: Georges Pompidou Prime Minister: Pierre Messmer 4 March – Legislative Election held. 11 March – Legislative Election held. 3 June – A Tupolev Tu-144 supersonic aircraft crashes at the Paris air show; 14 are killed. 11 July – Varig Flight 820 Boeing 707 crashes near Orly Airport, Paris, resulting in 123 deaths, with 11 survivors. 20 July – France resumes nuclear bomb tests in Mururoa Atoll, over the protests of Australia and New Zealand. 23 September – Cantonales Elections held.
Alpes-de-Haute-ProvenceAlpes-de-Haute-Provence or sometimes abbreviated as AHP (alp də ot pʁɔvɑ̃s; Aups d'Auta Provença; Alps of Upper Provence) is a department in the Provence-Alpes-Côte d'Azur region of France, bordering Alpes-Maritimes and Italy to the east, Var to the south, Vaucluse to the west, Drôme and Hautes-Alpes to the north. Formerly part of the province of Provence, it had a population of 164,308 in 2019, which makes it the 94th most populated French department.
Barneville-CarteretBarneville-Carteret (baʁnəvil kaʁtʁɛ) is a commune in the Manche department in the Normandy region of north-western France. For many years it has been a popular seaside resort destination. The commune resulted from a merger of two communes in 1964: Barneville-sur-Mer and Carteret whose port has ferry connections to the Channel Islands. The inhabitants of the commune are known as Barnevillais or Barnevillaises and Carteretais or Carteretaises.
Cinema of FranceFrench cinema consists of the film industry and its film productions, whether made within the nation of France or by French film production companies abroad. It is the oldest and largest precursor of national cinemas in Europe; with primary influence also on the creation of national cinemas in Asia. France continues to have a particularly strong film industry, due in part to protections afforded by the French government. In 2013, France was the second largest exporter of films in the world after the United States.
Olive oilOlive oil is a liquid fat obtained by pressing whole olives, the fruit of Olea europaea, a traditional tree crop of the Mediterranean Basin, and extracting the oil. It is commonly used in cooking for frying foods or as a salad dressing. It can also be found in some cosmetics, pharmaceuticals, soaps, and fuels for traditional oil lamps. It also has additional uses in some religions. The olive is one of three core food plants in Mediterranean cuisine, together with wheat and grapes.
Navier–Stokes equationsThe Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.
