Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those...

mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...

branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: Algebraic data type...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe") on a set X...

mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...

Algebraic notation is the standard method for recording and describing the moves in a game of chess. It is based on a system of coordinates to uniquely...

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until...

In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics...

Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models")...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the...

circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation...

equation), he has been described as the father or founder of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise...

In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with...

In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology...

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets...

mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations:...

and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics...

In universal algebra, an abstract algebra A is called simple if and only if it has no nontrivial congruence relations, or equivalently, if every homomorphism...