Definition:Abstract Algebra

Definition

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

• Definition:Linear Algebra

• 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 $\text {825}$$\text { CE}$, 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)

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Introduction
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (next): $\S 1$: Some very general remarks
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 26$. Introduction
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): abstract algebra
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebra: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): abstract algebra
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): abstract algebra
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): abstract algebra
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): abstract algebra