ideal
/aɪˈdi(ə)l/ noun C1- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
- A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
- A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
- 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.
- 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.
- A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
Plural ideals
From the library
The work to a man of my temperament was mechanical and uninteresting, but the privilege of living with youth, of helping to mould those young minds, and of impressing them with one’s own character and ideals was very dear to me.
“Gentlemen,” he said, “you will admit that, when arrived at a certain degree of fortune, the superfluities of life are all that can be desired; and the ladies will allow that, after having risen to a certain eminence of position, the ideal alone can be more exalted.
“Tell the gentleman that I need not repeat to him a description of my ideals.
I left the conservatory, and, at the same time, the rose and my ideal.
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