Finite ringIn mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent history. Although rings have more structure than groups, the theory of finite rings is simpler than that of finite groups.
Tensor product of modulesIn mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting in a third module, and also for a pair of a right-module and a left-module over any ring, with result an abelian group.
Idempotent (ring theory)In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that a = a2 = a3 = a4 = ... = an for any positive integer n. For example, an idempotent element of a matrix ring is precisely an idempotent matrix. For general rings, elements idempotent under multiplication are involved in decompositions of modules, and connected to homological properties of the ring.
Structure theorem for finitely generated modules over a principal ideal domainIn mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields.
Differential graded algebraIn mathematics, in particular in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. TOC A differential graded algebra (or DG-algebra for short) A is a graded algebra equipped with a map which has either degree 1 (cochain complex convention) or degree −1 (chain complex convention) that satisfies two conditions: A more succinct way to state the same definition is to say that a DG-algebra is a monoid object in the .
C*-algebraIn mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
RAF GrangemouthRoyal Air Force Grangemouth or more simply RAF Grangemouth is a former Royal Air Force station located north east of Falkirk, Stirlingshire, Scotland. It was opened as the Central Scotland Airport in May 1939 and operated as a Civilian Air Navigation School (CANS) until early September 1939. After the war it was used as Gliding School until 1946. It was then used by RAF Maintenance Command until its closure in June 1955.
Sylvain LéviSylvain Lévi (March 28, 1863 – October 30, 1935) was an influential French orientalist and indologist who taught Sanskrit and Indian religion at the École pratique des hautes études. Lévi's book Théâtre Indien is an important work on the subject of Indian performance art, and Lévi also conducted some of the earliest analysis of Tokharian fragments discovered in Western China. Lévi exerted a significant influence on the life and thought of Marcel Mauss, the nephew of Émile Durkheim.
NK KarlovacNK Karlovac 1919 is a Croatian football club based in the town of Karlovac. Karlovac plays their home matches at Stadion Branko Čavlović-Čavlek. Traditionally lower-level minnows, the club's most successful period in the Yugoslav football league system was in the 1970s when they competed in the Yugoslav Second League. After the breakup of Yugoslavia and the formation of the Croatian football league system in 1992 Karlovac spent most of the time playing in Druga HNL and Treća HNL, second and third levels.
Michel LaclotteMichel Laclotte (Saint Malo, France, 27 October 1929 – Montauban, 10 August 2021) was a French art historian and museum director, specialising in 14th and 15th century Italian and French painting. Laclotte's father, Pierre was a lawyer who died in 1940 fighting in the Second World War. His mother, Hugette (de Kermabon) took Michele and his sister to occupied Paris in 1941. He attended the lycée Henri-IV, then studied at the Sorbonne and the École du Louvre, and while still a student, began working at the museum as an intern in 1951.
