prealgebra

English

Alternative forms

• pre-algebra (especially the course)

Etymology

From pre- +‎ algebra.

Noun

prealgebra (countable and uncountable, plural prealgebras)

1. (US, education, uncountable) A school (in the US, middle school) course that introduces students to concepts needed to learn algebra.
   • 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.

   • 2002, Sally H. Spetz et al., REA's Practical Help for Pre-algebra, Research & Education Association, page 1:

     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.

   • 2011, Hal Torrance, Math Tutor: Pre-Algebra Skills, Mark Twain Media, page 1:

     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.

2. (mathematics, countable) A particular form of Lie algebra; also applied analogously to other types of algebra.
   • 1985, Robert C. Flagg, Church's Thesis is Consistent with Epistemic Arithmetic, Stewart Shapiro (editor), Intensional Mathematics, Elsevier Science Publishers, page 131,

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

   • 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 ${\mathsf {f}}:({\mathsf {A}},\alpha )\rightarrow ({\mathsf {B}},\beta )$ be a morphism of prealgebras.

   • 2011, M. Dubois-Violette, G. Landi, “Lie prealgebras”, in Alain Connes et al., editors, Contemporary Mathematics 546: Noncommutative Geometry and Global Analysis: Conference in Honor of Henri Moscovici, American Mathematical Society, page 131:

     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.

See also

• precalculus