identity element
81Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …
82Cayley table — A Cayley table, after the 19th century British mathematician Arthur Cayley, describes the structure of a finite group by arranging all the possible products of all the group s elements in a square table reminiscent of an addition or… …
83Lorentz group — Group theory Group theory …
84Exponentiation — Exponent redirects here. For other uses, see Exponent (disambiguation). Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent (or power) n. When n is a positive integer, exponentiation… …
85Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
86Kernel (algebra) — In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a matrix, also… …
87C*-algebra — C* algebras (pronounced C star ) are an important area of research in functional analysis, a branch of mathematics. The prototypical example of a C* algebra is a complex algebra A of linear operators on a complex Hilbert space with two additional …
88Universal algebra — (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ( models ) of algebraic structures.For instance, rather than take particular groups as the object of study, in universal… …
89Lattice (order) — See also: Lattice (group) The name lattice is suggested by the form of the Hasse diagram depicting it. Shown here is the lattice of partitions of a four element set {1,2,3,4}, ordered by the relation is a refinement of . In mathematics, a… …
90Moufang loop — In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by Ruth Moufang. Contents 1 Definition 2 Examples 3 Properties …
