Algebra is the branch of mathematics concerning the study of the rules of operations and the things which can be constructed from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Algebra is much broader than elementary algebra and studies what happens when different rules of operations are used and when operations are devised for things other than numbers. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields. Source: Wikipedia: Algebra.

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