Definition of "algebra" []

• 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 include an identity element, and the operations are commutative or associative. (noun)

American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

• "From the syntactic side, the free C-algebra B on a set X arises as a quotient of the term algebra formed from X (viewed as a set of variables) using the operation symbols and constants common to the algebras of C."
• "Indeed, the word "algebra" is derived from the title of this book: Kitab al-Jebr (The Book of Completion) in which he lays out for the first time the rules and steps of solving algebraic equations."
• "Wonderful goals and yet I can help but wonder if algebra is the best vehicle to accomplish these goals."