Definition of "abstract algebra"

abstract algebra

/ˈæbˌstɹækt ˈæl.d͡ʒɪ.bɹə/

noun
uncountable
1. (mathematics) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.
  Quotations
  The operations are necessarily algebraic, because the relative magnitudes of the given quantities and the quantity sought for are unknown; and it is the essential principle of abstract algebra to furnish rules and symbols of operation which are proper for calculating independently of the knowledge of relative magnitudes.
  1860, Prof. Challis, VIII: On the possibility of finding a Root, real or imaginary, of every Equation: The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, page 46
  This is neither the best nor the worst of the many abstract algebra texts written for advanced undergraduate courses. The author devotes 300 pages to a first course in abstract algebra and 200 pages to a (presumably) second course in linear algebra.
  1973, “AAAS Science Books: A Quarterly Review, Volume 9”, in American Association for the Advancement of Science, page 29