What is algebra?

• (noun): The mathematics of generalized arithmetical operations.

Algebra

Algebra is related to mathematics, but for historical reasons, the word "algebra" has three meanings as a bare word, depending on the context. The word also constitutes various terms in mathematics, showing more variation in the meaning. This article gives a broad overview of them, including the history.

Some articles on algebra:

Topological Algebra
... In mathematics, a topological algebra A over a topological field K is a topological vector space together with a continuous multiplication that makes it an algebra over K ... A unital associative topological algebra is a topological ring ... An example of a topological algebra is the algebra C of continuous real-valued functions on the closed unit interval, or more generally any Banach algebra ...
List Of Commutative Algebra Topics
... Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings ... geometry and algebraic number theory build on commutative algebra ...
Bivector - History
... was first defined in 1844 by German mathematician Hermann Grassmann in exterior algebra as the result of the exterior product of two vectors ... Clifford in 1888 added the geometric product to Grassmann's algebra, incorporating the ideas of both Hamilton and Grassmann, and founded Clifford algebra, that the ... Today the bivector is largely studied as a topic in geometric algebra, a Clifford algebra over real or complex vector spaces with a nondegenerate quadratic form ...
Initial Algebra - Use in Computer Science
... programming, such as lists and trees, can be obtained as initial algebras of specific endofunctors ... While there may be several initial algebras for a given endofunctor, they are unique up to isomorphism, which informally means that the "observable" properties of a data structure can be adequately captured by ... operations are Combined into one function, they give , which makes this an F-algebra for the endofunctor F sending to ...
Abstract Algebra - Rings and Fields
... A ring has two binary operations (+) and (×), with × distributive over + ... Under the first operator (+) it forms an abelian group ...