algebraické

Algebraická is an adjective in Czech meaning “algebraic.” It is the feminine singular form of the base adjective algebraický and is used to describe concepts that pertain to or arise from algebra, the branch of mathematics concerned with symbols and the rules for manipulating them. In mathematical Czech, algebraická is attached to nouns to form terms such as algebraická čísla, algebraická rovnice, algebraická funkce, algebraická struktura, and algebraická geometrie.

The term appears in a range of standard phrases. Algebraická čísla (algebraic numbers) are numbers that are roots of non-zero polynomials with rational coefficients. The set of algebraická čísla is countable, and it contrasts with transcendental numbers, which are not roots of any such polynomial. Algebraická rovnice (algebraic or polynomial equations) are equations in which the unknowns appear as roots of polynomials with coefficients in a given field. Algebraická funkce (algebraic function) refers to a function that satisfies a polynomial equation whose coefficients come from a fixed field. Algebraická struktura (algebraic structure) encompasses algebraic systems such as groups, rings, and fields. The term also appears in algebraická geometrie (algebraic geometry), a major area of modern mathematics studying geometric properties of solutions to polynomial equations.

Linguistic note: algebraická is formed from algebra and the suffixes used in Czech to create adjectives, and it mirrors the English term “algebraic” in mathematical usage.