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The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

A non-Abelian group, also sometimes known as a noncommutative group, is a group some of whose elements do not commute. The simplest non-Abelian group is the dihedral group ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

A geometry in which Archimedes' axiom does not hold.

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

An n×n matrix A is an elementary matrix if it differs from the n×n identity I_n by a single elementary row or column operation.