AbstractAlgebra

An abstract algebra is a mathematical system consisting of one or more sets of elements, together with one or more operations on these sets. Of course these aren't particularly interesting without some additional constraints as to how the operations behave. Some of the most important abstract algebrae are as follows:

• MathematicalGrouP
• RinGs and ModulEs
• FielDs and VectorSpaces
• AssociativeAlgebrae

A map between two algebrae that preserves the operations is called a HomoMorphism; if it is also a BiJection, it is called an IsoMorphism. Isomorphic algebrae are indistinguishable as far as the algebraic structure is concerned.

More will go here soon, including definitions of all these terms. Promise.