ideaalien
Ideaalien is the Dutch plural form used for the mathematical concept of ideals, particularly in ring theory. In modern Dutch texts the standard plural is usually idealen, while ideaalien may appear as an alternate form in some sources. In English-language mathematics, the corresponding concept is called an ideal (plural ideals).
Definition and basic idea. In a ring R, an ideal I is a subset that is an
Examples. In the ring of integers Z, the set nZ for any n ≥ 0 is an ideal.
Key properties and constructions. The sum and intersection of ideals are ideals, as is the product of
Usage and significance. Ideals provide a framework for studying decompositions, quotient structures, and homomorphic images in