Codomínio

Codomínio is a term used in mathematics, specifically in abstract algebra, to describe a specific type of algebraic structure that is the dual of a commutative ring. In essence, it is a set equipped with two binary operations, typically addition and multiplication, that satisfy a set of axioms. These axioms are derived from those of a commutative ring by reversing the roles of addition and multiplication and, in some definitions, also altering the identity elements.

A codomínio is characterized by having a commutative and associative multiplication operation with an identity element, and a commutative and associative addition operation. The distributive law holds, meaning multiplication distributes over addition. However, unlike a commutative ring, the addition operation in a codomínio does not necessarily have an identity element (a zero element), and the multiplication operation is not necessarily associative. The primary defining characteristic is that the structure satisfies the axioms of a commutative ring when the roles of addition and multiplication are swapped.

The concept of a codomínio is closely related to that of a coalgebra, which is a generalization of the concept. In some contexts, codomínios are used in the study of categories and their properties. While not as widely encountered as commutative rings, codomínios offer a different perspective on algebraic structures and are important in certain specialized areas of mathematics.