Algebriche

Algebriche is a term used in several Romance languages to denote objects or concepts that relate to algebra or are defined by algebraic relations. In Italian, algebriche is the feminine plural adjective agreeing with feminine nouns such as curve algebriche or funzioni algebriche; in Romanian, algebrice serves a similar function. In English, the direct cognate is algebraic, and the term is widely used in mathematics to describe properties defined by polynomial equations or algebraic structures.

In mathematics, algebraic refers to entities or properties expressible by polynomials with coefficients in a given field, typically the rational numbers or integers. Algebraic descriptions encompass a broad range of objects, including algebraic numbers, algebraic curves, and algebraic varieties. The term is also used to classify mathematical structures whose operations satisfy algebraic axioms.

Algebriche structures, such as groups, rings, fields, modules, and algebras, are fundamental in algebra and its applications. These structures are defined by operations and axioms, and many questions concern their relationships, representations, and classifications. In geometry and number theory, the area of algebraic geometry studies solutions to polynomial equations and the shapes they form, with algebraic curves as one-dimensional examples.

Algebraic numbers are roots of nonzero polynomials with integer coefficients. By contrast, numbers that are not algebraic are called transcendental. The distinction between algebraic and transcendental underpins results across fields, including theory of numbers and analysis.

Overall, algebriche language reflects how many mathematical concepts are organized around algebraic definitions, polynomials, and the structural framework of algebra.