Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization...

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...

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...

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

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

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 mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement...

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...

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...

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

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

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

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

algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is...

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...

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

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

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...

algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...

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...

Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both...

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

In mathematics: In abstract algebra and mathematical logic a derivative algebra is an algebraic structure that provides an abstraction of the derivative...

algebra Enveloping algebra, of an associative algebra: see Associative algebra § Enveloping algebra Enveloping von Neumann algebra, of a C*-algebra This...

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...

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...