Idealn

Idealn is not a standard, widely recognized term in mathematics or other disciplines. In practice, it is sometimes used as a placeholder name for a concept that involves a family or sequence of ideals indexed by n, or as shorthand for an ideal generated by n elements. Because there is no universal definition, the exact meaning of idealn depends on the author and the context in which it appears.

In ring theory, idealn can denote an indexed family of ideals I_n in a ring R. For example, one might define I_n to be a certain ideal associated with a parameter n, such as a family of principal ideals (n) in the ring of integers, or a chain of ideals coming from a filtration. Another common interpretation is that idealn refers to an ideal generated by n elements, often written as (a_1, a_2, ..., a_n), where the generating set size is explicit in the context.

Examples help illustrate these ideas. In the ring Z, the ideal generated by the integer n is the principal ideal (n); if someone writes I_n = (n), this is an indexed family of ideals parametrized by n. In a polynomial ring k[x_1, ..., x_m], the ideal generated by a set of n polynomials f_1, ..., f_n can be denoted (f_1, ..., f_n) and thought of as an idealn in that context.

Because idealn lacks a single canonical definition, readers should consult the specific text for the precise meaning. See also ideal, principal ideal, generated ideal, and powers or filtrations I^n.