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A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

Define E(x;q,a)=psi(x;q,a)-x/(phi(q)), (1) where psi(x;q,a)=sum_(n<=x; n=a (mod q))Lambda(n) (2) (Davenport 1980, p. 121), Lambda(n) is the Mangoldt function, and phi(q) is ...

A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that x in muB for all mu in F with |mu|>=lambda, where F is the ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

Let A be any algebra over a field F, and define a derivation of A as a linear operator D on A satisfying (xy)D=(xD)y+x(yD) for all x,y in A. Then the set D(A) of all ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When codewords are chosen ...

A multilinear form on a vector space V(F) over a field F is a map f:V(F)×...×V(F)->F (1) such that c·f(u_1,...,u_i,...,u_n)=f(u_1,...,c·u_i,...,u_n) (2) and ...