##### Wiktionary

**abstract algebra**

n. (context mathematics English) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.

##### Wikipedia

**Abstract algebra**

Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a powerful formalism for analyzing and comparing different algebraic structures.

Universal algebra is a related subject that studies the nature and theories of various types of algebraic structures as a whole. For example, universal algebra studies the overall theory of groups, as distinguished from studying particular groups.

#### Usage examples of "abstract algebra".

If cryptography is a form of __abstract algebra__, then inventing a new cipher system is nothing more than building abstract castles in the air with material and design of one's own choosing.