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"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

A differential k-form omega of degree p in an exterior algebra ^ V is decomposable if there exist p one-forms alpha_i such that omega=alpha_1 ^ ... ^ alpha_p, (1) where alpha ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k=1)^p of cardinal number p are the 2^p Boolean functions B_1B_2...B_p=B_1 intersection B_2 ...

In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...