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Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

Abstract Algebra