algebra

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
• noun A set together with a pair of binary operations defined on the set. Usually, the set and the operations simultaneously form both a ring and a module.

from The Century Dictionary.

• noun Algebra of multiple units.
• noun Formal mathematics; the analysis of equations; the art of reasoning about relations, more especially quantitative relations, by the aid of a compact and highly systematized notation.
• noun Any special system of notation adapted to the study of a special system of relationship: as, “it is an algebra upon an algebra,” Sylvester.
• noun A treatise on algebra.
• noun Its abbreviation is algebra

from the GNU version of the Collaborative International Dictionary of English.

• noun (Math.) 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun uncountable, mathematics A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
• noun uncountable, mathematics The study of algebraic structures.
• noun countable, mathematics A universal algebra.
• noun countable, algebra An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear.
• noun countable, set theory, 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 countable, mathematics One of several other types of mathematical structure.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun the mathematics of generalized arithmetical operations