algebra
UK /ˈæl.dʒɪ.bɹə/ · US /ˈæl.d͡ʒɪ.bɹə/ noun
Forms algebras
- noun (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- noun (uncountable, mathematics, sometimes capitalized) 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).
- noun A universal algebra.
- noun 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.
- noun (countable, set theory, mathematical analysis) 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).
- noun (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.
- noun (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
Synonyms
algebra over a field algebra over a ring field of sets algebra of sets
Etymology
Borrowed from Medieval Latin algebra, from the Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الْكِتَاب الْمُخْتَصَر فِي حِسَاب الْجَبْر وَالْمُقَابَلَة (al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).
Webster’s 1913
- noun That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
- noun A treatise on this science.
Etymology [LL. algebra, fr. Ar. al-jebr reduction of parts to a whole, or fractions to whole numbers, fr. jabara to bind together, consolidate; al-jebr w'almuqabalah reduction and comparison (by equations): cf. F. algèbre, It. & Sp. algebra.]
Sources: Wiktionary · Webster’s 1913 — from the Wiktionary entry “algebra”, CC BY-SA 4.0. Details