algebra

Meaning

1. (uncountable) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
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) Any of several objects of study in Algebra
4. (countable, uncountable) Any of several objects of study in Algebra
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).
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.
7. (historical, rare, uncountable) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.

Synonyms

arithmetic

geometry

mathematics

alg

hypercomplex system

Translations

algèbre

Algebra

álgebra

álgebra

algebra

algebra

άλγεβρα

àlgebra

cebir

stelkunde

Άλγεβρα

Álgebra

Buchstabenrechnung

ars per litteras supputandi

Pronounced as (IPA)

/ˈæl.dʒɪ.bɹə/

Etymology

Borrowed from Medieval Latin algebra, from the Arabic word 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”).

Sentences

Quantum deformations of the universal enveloping algebra lead to the notion of quantum groups .