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A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

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 ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

A solenoidal vector field satisfies del ·B=0 (1) for every vector B, where del ·B is the divergence. If this condition is satisfied, there exists a vector A, known as the ...

The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n,F). If p is prime and F is the finite field of order q=p^m, S(n,q) is written instead ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

Let k be a field of finite characteristic p. Then a polynomial P(x) in k[x] is said to be additive iff P(a)+P(b)=P(a+b) for {a,b,a+b} subset k. For example, P(x)=x^2+x+4 is ...

An anchor is the bundle map rho from a vector bundle A to the tangent bundle TB satisfying 1. [rho(X),rho(Y)]=rho([X,Y]) and 2. [X,phiY]=phi[X,Y]+(rho(X)·phi)Y, where X and Y ...

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...