algebras

Noun

algebra (countable and uncountable, plural 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.1551, James A.H. Murray, editor, A New English Dictionary on Historical Principles: Founded Mainly on the Materials Collected by the Philological Society., volume 1, Oxford: Clarendon Press...
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. A universal algebra.
4. 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.

   Synonyms:

   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).

   Synonyms:

   field of sets, algebra of sets

6. (figuratively) 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, William Clark, edited by William Hugh Logan, Marciano; or, The discovery: A tragi-comedy, Edinburgh: Reprinted for Private Circulation, published 1871, →ISBN, page 13

See all 7 meanings of algebra