noun Download 🔗Share A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. Examples : "Even though it's hard, Maria strives to live up to her ideals of honesty and kindness in her everyday actions. " value philosophy moral quality attitude being character Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share A subring closed under multiplication by its containing ring. Examples : "In abstract algebra, ideals are special subsets within a ring that absorb multiplication from the larger ring. " math technical Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share (lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins). Examples : "The study of ideals in lattice theory helps mathematicians understand how sets of elements are organized and related based on specific rules of inclusion and combination. " theory math logic system Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection. Examples : "The mathematician studied ideals of numbers, focusing on collections where adding or reducing elements always resulted in another member of the same collection. " math Chat with AIVocabulary GamePractice Reading
noun Download 🔗Share (Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍. Examples : "Within the Lie algebra that describes a rotating object's movements, the ideals represent specific ways the object can rotate that, when combined with any other possible movement of the object, still result in one of those specific rotations. " theory math Chat with AIVocabulary GamePractice Reading
