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The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

Let L be an extension field of K, denoted L/K, and let G be the set of automorphisms of L/K, that is, the set of automorphisms sigma of L such that sigma(x)=x for every x in ...

A generalization of the Fibonacci numbers defined by 1=G_1=G_2=...=G_(c-1) and the recurrence relation G_n=G_(n-1)+G_(n-c). (1) These are the sums of elements on successive ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

The Gergonne point Ge is the perspector of a triangle DeltaABC and its contact triangle DeltaT_AT_BT_C. It has equivalent triangle center functions alpha = [a(b+c-a)]^(-1) ...

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. ...

The Hankel transform (of order zero) is an integral transform equivalent to a two-dimensional Fourier transform with a radially symmetric integral kernel and also called the ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...