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Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian mathematician, astronomer, astrologer and geographer, Muhammad bin Mūsā al-Khwārizmī titled Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing "), which provided symbolic operations for the systematic solution of linear and quadratic equations.Classi fication · Elementary algebra · Abstract algebra · Objects called algebras

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In mathematics, an algebra over a field K, or a K-algebra, is a vector space A over K equipped with a compatible notion of multiplication of elements of A. A straightforward generalisation allows K to be any commutative ring. (Some authors use the term "algebra&qu ot; synonymously with "associativ e algebra", but this article does not.Definitions · Kinds of algebras and ... · Algebras and rings