algébricas

Algébricas is the Portuguese and Spanish term commonly used to refer to objects, structures, or concepts that are defined by algebraic equations. In mathematics, the adjective “algébrica” characterises entities that can be described as the zero set of one or more polynomial expressions with coefficients in a given field, typically the rational, real, or complex numbers. The scope of the notion includes algebraic numbers, algebraic functions, algebraic curves, algebraic varieties, and algebraic groups, among others, each playing a central role in various branches of mathematics.

An algebraic number is a complex number that satisfies a non‑zero polynomial equation with rational coefficients. The collection of all algebraic numbers forms a field that is algebraically closed only after adjoining all possible algebraic extensions, leading to the concept of the algebraic closure of a field. Algebraic functions extend this idea to functions that satisfy polynomial relations with respect to their arguments; they are fundamental in the study of complex analysis and algebraic geometry.

Algebraic curves are one‑dimensional algebraic varieties, defined as the set of solutions to a single polynomial equation in two variables. Higher‑dimensional analogues, called algebraic varieties, are central objects in algebraic geometry, where tools such as sheaf cohomology and scheme theory are employed to investigate their properties. Algebraic groups combine group structure with algebraic variety structure, providing a framework for studying symmetry in a polynomial context.

The term “algébricas” is therefore a linguistic shortcut that encapsulates a wide array of mathematically rigorous concepts, all unified by the requirement that they be describable through polynomial equations. This common foundation enables powerful interactions between number theory, geometry, and algebra.