• Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization...
    120 KB (11,825 words) - 01:56, 28 March 2024
  • 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...
    73 KB (9,399 words) - 18:08, 23 March 2024
  • Thumbnail for Linear algebra
    Linear algebra is the branch of mathematics concerning linear equations such as: a1x1+⋯+anxn=b,{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,} linear...
    64 KB (7,687 words) - 19:56, 24 January 2024
  • Thumbnail for Abstract algebra
    mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...
    32 KB (4,165 words) - 01:45, 7 January 2024
  • branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: Algebraic data type...
    1 KB (238 words) - 13:14, 27 August 2020
  • mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...
    11 KB (1,331 words) - 10:03, 10 March 2024
  • Thumbnail for Lie algebra
    In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g{\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...
    61 KB (10,013 words) - 21:10, 26 March 2024
  • Thumbnail for Exterior algebra
    In mathematics, the exterior algebra or Grassmann algebra of a vector space V{\displaystyle V} is an associative algebra that contains V,{\displaystyle...
    77 KB (11,558 words) - 12:46, 26 March 2024
  • Thumbnail for Algebraic notation (chess)
    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...
    22 KB (2,582 words) - 08:17, 24 March 2024
  • 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...
    30 KB (5,139 words) - 13:11, 26 March 2024
  • mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...
    20 KB (2,798 words) - 14:57, 7 December 2023
  • 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...
    22 KB (2,875 words) - 03:27, 1 November 2023
  • a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize...
    63 KB (8,652 words) - 08:02, 13 March 2024
  • Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until...
    120 KB (16,629 words) - 10:42, 27 March 2024
  • 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...
    31 KB (4,457 words) - 22:45, 18 March 2024
  • In database theory, relational algebra is a theory that uses algebraic structures for modeling data, and defining queries on it with a well founded semantics...
    50 KB (6,121 words) - 13:39, 19 February 2024
  • In mathematics, an algebra homomorphism is a homomorphism between two algebras. More precisely, if A and B are algebras over a field (or a ring) K, it...
    3 KB (423 words) - 11:15, 30 January 2024
  • algebra (also known as a Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is...
    93 KB (13,242 words) - 00:17, 24 March 2024
  • Thumbnail for Al-Khwarizmi
    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...
    73 KB (7,409 words) - 03:26, 16 March 2024
  • Mathematics (section Algebra)
    in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among...
    167 KB (16,256 words) - 20:03, 18 March 2024
  • universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...
    20 KB (2,675 words) - 03:41, 20 July 2023
  • Communications in Algebra is a monthly peer-reviewed scientific journal covering algebra, including commutative algebra, ring theory, module theory, non-associative...
    2 KB (119 words) - 15:39, 18 July 2023
  • Thumbnail for Lie group
    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...
    64 KB (9,356 words) - 19:52, 2 March 2024
  • Thumbnail for Computer algebra
    In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the...
    24 KB (2,925 words) - 18:59, 12 March 2024
  • In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...
    99 KB (13,383 words) - 08:14, 22 March 2024
  • algebra Enveloping algebra, of an associative algebra: see Associative algebra § Enveloping algebra Enveloping von Neumann algebra, of a C*-algebra This...
    358 bytes (74 words) - 23:29, 29 December 2023
  • 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...
    51 KB (7,469 words) - 16:18, 14 March 2024
  • In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction...
    7 KB (782 words) - 03:56, 7 January 2024
  • Thumbnail for Vector space
    also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector...
    88 KB (11,305 words) - 17:06, 18 March 2024
  • 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...
    2 KB (212 words) - 14:01, 6 March 2022