Definition:Abstract Algebra

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Abstract algebra is a branch of mathematics which studies algebraic structures and algebraic systems.

It can be roughly described as the study of sets equipped with operations.

Also known as

Abstract algebra is also sometimes referred to as modern algebra, particularly in older texts.

Also see

  • Results about abstract algebra can be found here.

Linguistic Note

The word algebra originates from the Arabic word al-ğabr, meaning balancing, reduction or restoration.

It originates from the name of a book, circa $825$ C.E., by Muhammad ibn Musa al-Khwarizmi:

Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala (The Compendious Book on Calculation by Completion and Balancing)