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1.the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.

2.any of several algebraic systems, esp. a ring in which elements can be multiplied by real or complex numbers (linear algebra) as well as by other elements of the ring.

3.any special system of notation adapted to the study of a special system of relationship: algebra of classes. - Algebra Definition