plural of algebraic group

(algebraic geometry) A group that is an algebraic variety.

(algebra, ring theory) An algebra over a reduced ring.

plural of algebraic extension

(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.

(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.

(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.