Abstract Algebra is the branch of algebra in which the r esults and methods of general algebra are extended to a number of other algebraic systems, such as groups, fields , rings, vector spaces, and algebras over a field . The term abstract algebra was coined in the early 19th century. Since then, it has been used for new disciplines that have evolved by extending the original scope of algebra. Today, abstract algebra is also known as modern algebra as it comprises many of the new developments in algebra
Abstract algebra studies sets with discrete structures and operations on them. The most familiar example is the integers: sets that contain the numbers from 0 to 9, with addition and multiplication as operations. Another example is vector spaces, which feature scalar products for composition of linear maps between vector spaces, in a manner similar to coordinate space composition of functions.
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