ideals background

ideals

/aɪˈdɪəlz/ /aɪˈdi.əlz/

Illustration ideals - Image 1

Illustration ideals - Image 2

noun

Ideales, modelos

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. "

Aunque es difícil, María se esfuerza por vivir de acuerdo con sus ideales de honestidad y bondad en sus acciones diarias.

value philosophy moral quality attitude being character

Illustration ideals - Image 1

noun

Ideal

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. "

En álgebra abstracta, los ideales son subconjuntos especiales dentro de un anillo que absorben la multiplicación del anillo más grande.

Illustration ideals - Image 1

noun

Ideal

(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. "

El estudio de los ideales en la teoría de retículos ayuda a los matemáticos a comprender cómo se organizan y relacionan los conjuntos de elementos en función de reglas específicas de inclusión y combinación.

theory math logic system

Illustration ideals - Image 1

noun

Ideales

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. "

El matemático estudió los ideales de los números, centrándose en colecciones donde sumar o reducir elementos siempre resultaba en otro miembro de la misma colección.

Illustration ideals - Image 1

noun

Ideal

(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. "

Dentro del álgebra de Lie que describe los movimientos de un objeto giratorio, los ideales representan formas específicas en que el objeto puede rotar que, cuando se combinan con cualquier otro movimiento posible del objeto, aún resultan en una de esas rotaciones específicas.