In commutative algebra, the idealizer is related to a more general construction.

Mother, the idealizer, tried for gentrification - "Don't make waves."

The idealizer in a semigroup or ring is another construction that is in the same vein as the centralizer and normalizer.

(cf. idealizer in abstract algebra.)

If the film had been entirely his, Mr. Bergman, an idealizer of women, would have brought forth an essential and forgivable core of womanliness in Marianne.

Leon Battista Alberti was an early idealizer, stressing the typical, with others such as Michelangelo supporting selection of the most beautiful - he refused to make portraits for that reason.

In abstract algebra, the idealizer of a subsemigroup T of a semigroup S is the largest subsemigroup of S in which T is an ideal.

While this is the standard usage of the term "normalizer" in Lie algebra, it should be noted that this construction is actually the idealizer of the set S in .

Often, when right or left ideals are the additive subgroups of R of interest, the idealizer is defined more simply by taking advantage of the fact that multiplication by ring elements is already absorbed on one side.

He was no idealizer of the perfections of the market - he never called the Invisible Hand, the most celebrated metaphor in economics, "divine," although some of his epigones did turn worship of the free market into a quasi theology.