Page "Pure mathematics" Paragraph 21

Abstract algebra is not to be confused with the manipulation of formulae that is covered in secondary education.

It studies sets together with binary operations defined on them.

Sets and their binary operations may be classified according to their properties: for instance, if an operation is associative on a set that contains an identity element and inverses for each member of the set, the set and operation is considered to be a group.

Other structures include rings, fields and vector spaces.