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 (2,935 words) - 02:08, 13 August 2024
, that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie...
61 KB (10,457 words) - 07:08, 29 August 2024
A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...
25 KB (2,964 words) - 22:33, 1 September 2024
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero...
8 KB (1,153 words) - 17:39, 1 May 2024
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 of A. This is thus...
30 KB (4,256 words) - 10:18, 18 August 2024
is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory. Fields of sets play an essential...
23 KB (3,675 words) - 13:27, 30 October 2023
related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A which is simple, and for which...
8 KB (1,134 words) - 12:54, 1 September 2022
operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas...
87 KB (10,299 words) - 08:01, 21 August 2024
mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix...
10 KB (1,532 words) - 15:42, 21 February 2024
elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined...
32 KB (4,185 words) - 14:05, 4 June 2024