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

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

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

multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras where associativity of multiplication is assumed...

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...

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

c)-(a\cdot b)\cdot c=0} . But, there are algebras R {\displaystyle R} which are not necessarily associative, meaning if a , b , c ∈ R {\displaystyle a...

{\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...

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...

which there is no requirement for multiplication to be associative. For these authors, every algebra is a "ring". The most familiar example of a ring is...

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...

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

In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we...

may be regarded as a free commutative algebra. For R a commutative ring, the free (associative, unital) algebra on n indeterminates {X1,...,Xn} is the...

and associative then B is associative. If A is associative and x + x*, xx* associate and commute with everything, then B is an alternative algebra. Schafer...

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have x...

In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital)...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

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...

n = 1 , … , k {\displaystyle R\ /\ I_{n},\;n=1,\ldots ,k} ⁠. An associative algebra A {\displaystyle A} over a commutative ring R {\displaystyle R} is...

category-theoretic sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams...

In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...

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

algebras A and B, an algebra homomorphism f : A → B is unital if it maps the identity element of A to the identity element of B. If the associative algebra...

project began in 1872 when Benjamin Peirce first published his Linear Associative Algebra, and was carried forward by his son Charles Sanders Peirce. Most...

the group product in G. The definition for associative algebras is analogous, except that associative algebras do not always have an identity element, in...

In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative...

space over K which is both a unital associative algebra and a counital coassociative coalgebra.: 46  The algebraic and coalgebraic structures are made...

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

theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice...