Definition of "algebraic"

Of, or relating to, algebra.  examples

(mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.  examples

(algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.  examples

(algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.  examples

(chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.  examples