article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification...
30 KB (4,256 words) - 10:18, 18 August 2024
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
multiplication are associative, but not (generally) commutative. Associative operations are abundant in mathematics; in fact, many algebraic structures (such...
25 KB (3,391 words) - 23:57, 8 August 2024
multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras. Given an integer...
22 KB (2,935 words) - 02:08, 13 August 2024
yb. For associative algebras, the definition can be simplified as follows: a non-zero associative algebra over a field is a division algebra if and only...
8 KB (1,153 words) - 17:39, 1 May 2024
In mathematics, a composition algebra A over a field K is a not necessarily associative algebra over K together with a nondegenerate quadratic form N...
11 KB (1,319 words) - 21:33, 29 August 2024
{\displaystyle [x,y]} . A Lie algebra is typically a non-associative algebra. However, every associative algebra gives rise to a Lie algebra, consisting of the same...
61 KB (10,457 words) - 07:08, 29 August 2024
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...
64 KB (9,171 words) - 11:01, 7 August 2024
where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with...
11 KB (1,359 words) - 23:57, 25 May 2024
algebra of observables of any quantum system should be a formally real algebra that is commutative (xy = yx) and power-associative (the associative law...
19 KB (2,492 words) - 22:29, 1 September 2024