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A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique ...

The proposition that every proper ideal of a Boolean algebra can be extended to a maximal ideal. It is equivalent to the Boolean representation theorem, which can be proved ...

The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n in Z and i in {0,1,2,3,...} there are ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

The terms "measure," "measurable," etc. have very precise technical definitions (usually involving sigma-algebras) that can make them appear difficult to understand. However, ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...