algebra

noun algebras

1. uncountable 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.
2. capitalized, sometimes, uncountable 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. countable, uncountable A universal algebra.
4. countable, uncountable 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.

   Similar: algebra over a field, algebra over a ring

5. countable 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).

   Similar: field of sets, algebra of sets

6. countable, figuratively, uncountable 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?
7. historical, rare, uncountable The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture. Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate, til viij. daies ben goon in þe wyntir, & v. in þe somer; for þanne it schal make quytture, and be sikir from swellynge; & þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be sei