Algebra: Meaning (information, definition, explanation, facts)

Algebra (from the Arabic "al-jabr" meaning "reunion", "connection" or "completion") is a branch of mathematics which may be defined as a generalization and extension of arithmetic. The field may be roughly divided in

• elementary algebra, where the properties of operations on the real number system are recorded, symbols are used as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied,
• abstract algebra, where algebraic structures such as groups, rings and as fields are axiomatically defined and investigated.
• The specific properties of vector spaces are studied in linear algebra.
• universal algebra, where those properties common to all algebraic structures are studied.
• computer algebra, where algorithms for the symbolic manipulation of mathematical objects are collected

The word algebra is also used for various algebraic structures:

• algebra over a field
• Boolean algebra
• sigma-algebra