ideals

"Even though it's hard, Maria strives to live up to her ideals of honesty and kindness in her everyday actions. "

"In abstract algebra, ideals are special subsets within a ring that absorb multiplication from the larger ring. "

"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. "

"The mathematician studied ideals of numbers, focusing on collections where adding or reducing elements always resulted in another member of the same collection. "

"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. "