Prealgebra

2000, Alfred S. Posamentier, Making Pre-Algebra Come Alive, Sage Publications (Corwin Press), page 1, In most secondary school curricula, pre-algebra is the last course in which specific attention is paid to multiplication, division, squares, cubes, and primes. Thereafter, these skills and operations are pretty much taken for granted.

Almost everyone pursuing a career or a course of study needs to know pre-algebra math. Also, almost all college entrance tests and professional exams require knowledge of at least pre-algebra math. The practicing of almost all crafts involves the use of pre-algebra math.

Pre-algebra is considered to be something of a terminal arithmetic course. What this means for the student is that pre-algebra is a course that links many topics together before the student proceeds to more abstract mathematics courses.

2006, Oswald Wyler, Algebraic Theories of Continuous Lattices, Bernhard Banaschewski, Rudolf-Eberhard Hoffmann (editors), Continuous Lattices, Springer, Lecture Notes in Mathematics 871, page 398, Let mathsf f:( mathsf A,α)→( mathsf B,β) be a morphism of prealgebras.

Conversely, if H is a complete preorder which satisfies the #92;land,#92;lor-distributive law, then, by the Adjoint Functor Theorem, H is a Heyting prealgebra.

It turns out that the duality of Theorem 6 restricts as a duality between Lie prealgebras and the category of differential quadratic Koszul Frobenius algebras.