Explore: Ideals

Look up Ideal, ideal, or ideals in Wiktionary, the free dictionary. Ideal may refer to: Ideal (ethics), values that one actively pursues as goals Platonic

to rings, attach more naturally to the ideals than to the elements of the ring. For instance, the prime ideals of a ring are analogous to prime numbers

{I}}} . Since prime ideals are radical ideals, p n = p {\displaystyle {\sqrt {{\mathfrak {p}}^{n}}}={\mathfrak {p}}} for any prime ideal p {\displaystyle

number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is

An ideal is a principle or value that one actively pursues as a goal, usually in the context of ethics, and one's prioritization of ideals can serve to

right ideal of R with {0} ⊆ K ⊆ N, then either K = {0} or K = N. N is a simple right R-module. Minimal ideals are the dual notion to maximal ideals. Many

𝜎-ideal, or sigma ideal, of a σ-algebra (𝜎, read "sigma") is a subset with certain desirable closure properties. It is a special type of ideal. Its

primitive ideals are always two-sided ideals. Primitive ideals are prime. The quotient of a ring by a left primitive ideal is a left primitive ring. For commutative

fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both

In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient (I : J) is the set ( I : J ) = { r ∈ R ∣ r J ⊆ I } {\displaystyle