plural of reduced algebra

(mathematics, education) An informally defined area of algebra considered suitable to be taught to secondary school students.

plural of Hurwitz algebra

(algebra) Any one of the unital composition algebras identified by Hurwitz's theorem (on composition algebras) as solutions to the Hurwitz problem.

plural of composition algebra

(algebra) A non-associative (not necessarily associative) algebra, A, over some field, together with a nondegenerate quadratic form, N, such that N(xy) = N(x)N(y) for all x, y ∈ A.

(algebra) A vector space over some field which also has an associative vector-valued multiplication operator between vectors which together with the abelian group feature of the vector space makes a ring.

(algebra) A bounded distributive lattice with a dual endomorphism (where “dual” means that it satisfies De Morgan’s laws).

(algebra) A linear algebra such that its non-zero vectors form a multiplicative group.

(mathematics) A generalization of central simple algebras to R-algebras where R need not be a field.