article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification...

non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative....

multiplication are associative, but not (generally) commutative. Associative operations are abundant in mathematics; in fact, many algebraic structures (such...

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...

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...

{\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...

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...

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...

. Every associative algebra is power-associative, but so are all other alternative algebras (like the octonions, which are non-associative) and even...

algebra of observables of any quantum system should be a formally real algebra that is commutative (xy = yx) and power-associative (the associative law...