ideal
ideal (noun) synonyms
ideal definitions
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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.
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A subring closed under multiplication by its containing ring.
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A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
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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.
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A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
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A Lie subalgebra (subspace that is closed under the Lie bracket) ๐ of a given Lie algebra ๐ such that the Lie bracket [๐,๐] is a subset of ๐.