Coideal

Translation of "coideal" into Russian

Noun

/kəʊˈaɪdiəl/

/koʊˈaɪdiəl/

coideal

coideals pl

коидеал

матем., спец.

This subspace is a coideal of the coalgebra C.

Это подпространство является коидеалом коалгебры C.

Adjective

coideal

more coideal Comp.

most coideal Super.

Used mainly attributively in mathematical contexts.

коидеальный

матем., спец.

The coideal property is essential in this proof.

Коидеальное свойство важно в этом доказательстве.

Noun

In coalgebra theory, a linear subspace of a coalgebra that is stable under the comultiplication and counit, serving as the dual notion of an ideal.

Let C be a coalgebra; the subspace spanned by x in C = k[x]/(x²) is a coideal.

In order theory, the complement of an ideal in a partially ordered set; an upward-closed set of elements.

The set of cofinite subsets of ℕ forms a coideal in the Boolean algebra of all subsets of ℕ.

Adjective

Relating to or having the properties of a coideal.

The coideal condition guarantees that the subspace is compatible with the coalgebra structure.