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An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

The function from a given nonempty set X to the power set P(X) that maps every element x of X to the set {x}.

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

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 ...

A cycle graph of a group is a graph which shows cycles of a group as well as the connectivity between the cycles. Such graphs are constructed by drawing labeled nodes, one ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...