(algebra, field theory) A field extension L/K which is algebraic over K (i.e., is such that every element of L is a root of some (nonzero) polynomial with coefficients in K).

(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 algebraic poset

(algebra, order theory) A partially ordered set (poset) in which every element is the supremum of the compact elements below it.

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, field theory) (Of a subset S of the extension field L of a given field extension L / K) whose elements do not satisfy any non-trivial polynomial equation with coefficients in K.

(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.