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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 ...

Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

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 ...

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...

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 ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

A polynomial map phi_(f), with f=(f_1,...,f_n) in (K[X_1,...,X_n])^m in a field K is called invertible if there exist g_1,...,g_m in K[X_1,...,x_n] such that ...