Definitions for idealizer
This page provides all possible meanings and translations of the word idealizer
Random House Webster's College Dictionary
i•de•al•izeaɪˈdi əˌlaɪz(v.)-ized, -iz•ing.
(v.t.)to consider or represent as having qualities of ideal perfection or excellence.
to represent in an ideal form or character.
(v.i.)to represent something in an ideal form.
Origin of idealize:
A person who idealizes
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. Such an idealizer is given by In ring theory, if A is an additive subgroup of a ring R, then is the largest subring of R in which A is a two-sided ideal. In Lie algebra, if L is a Lie ring with Lie product [x,y], and S is an additive subgroup of L, then the set is classically called the normalizer of S, however it is apparent that this set is actually the Lie ring equivalent of the idealizer. It is not necessary to mention that [S,r]⊆S, because anticommutativity of the Lie product causes [s,r] = −[r,s]∈S. The Lie "normalizer" of S is the largest subring of S in which S is a Lie ideal.
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