prealgebra

plural prealgebras · alternative pre-algebra

1. USuncountableeducationA school (in the US, middle school) course that introduces students to concepts needed to learn algebra.

   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.

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

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   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.

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

2. countablemathematicsA particular form of Lie algebra; also applied analogously to other types of algebra.

   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.

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   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.

   1985, Robert C. Flagg, “Church's Thesis is Consistent with Epistemic Arithmetic”, in Stewart Shapiro, editor, Intensional Mathematics, Elsevier Science Publishers, 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.

   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