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An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

An associative ring, also called a Hecke ring, which has a technical definition in terms of commensurable subgroups.

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

One of the basic objects treated in a given formal language system. The term is sometimes also used as a synonym for urelement.

If the property of being an object is expressed by a basic predicate of the system, then such a predicate (if it exists) is called a universal predicate, or universal ...