algebra

noun8

1. •
   Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.

   • Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber. — 1551
2. •
   Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
3. •
   (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.

   • Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what? — 1663
4. •
   Any of several objects of study in Algebra
5. •
   A universal algebra.
6. •
   An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
7. •
   A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
8. •
   (rare, historical) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.

   • Algebra is used today by surgeons to mean bone-setting, i.e. the restoration of bones, and the idea of restoration is present in the mathematical context, too. — 1987