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Algebra is the branch of mathematics that uses numbers, letters and signs to generalize several algebraic arithmetic/structures operations. The term comes from the latin algĕbra which, in turn, derives from an Arabic word which means "reduction".

Etymological origins in past, where was meant by algebra art to reduce moved or fractured bones. However, this sense became obsolete.

Nowadays, algebra refers to the branch of mathematics that studies the structures, relationships, and the quantities. Elementary algebra is the one that handles arithmetic operations (addition, subtraction, multiplication, division) but which, unlike the arithmetic, uses symbols (a, x, y) instead of numbers (1, 2, 9). Thus, it is possible to formulate general laws and to designate variables (say unknown) allowing to develop equations and analysis that corresponds to their resolution.

Algebra elemental (or classical) postulated many laws that allow to know the properties of arithmetic operations. For example, the addition (a + b) is commutative (a + b = b + a), associative, has an inverse operation (subtract) and has an identity element (0).

Some of these properties are shared by other operations (for example, the multiplication is also commutative and associative).

This is the fundamental theorem of algebra which States that any polynomial in a non-const variable with complex coefficients has as many roots as its degree, given that the roots may be multiple. It assumes that the field of complex numbers is split/clos to the operations of the algebra.