Definitions for idealizer
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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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